Isn't it a kind of a trap for integers?

Algebra Level 4

\[ {\left| { \Large \sum\limits_{m = 0}^{123456789} {{i^{m - 4\left\lfloor {\frac{m}{4}} \right\rfloor }}} } \right|^2} = \, ? \]

Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.

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