Find the number of ordered \(2014\)-tuples of integers \( (x_1,x_2, \ldots, x_{2014}) \) such that

\( x_1 + x_2 + \ldots +x_{2014} \geq {2014}^2 \ \text{and} \ x_1^2 + x_2^2 + \ldots + x_{2014}^2 \leq {2014}^3 + 1 \).

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