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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def aux_dict(self):
 """Get dictionary representation of auxiliary states arrays. Returns ------- aux_dict : dict of str to NDArray The dictionary that maps name of auxiliary states to NDArrays. Raises ------ ValueError : if there are duplicated names in the auxiliary states. """

        if self._aux_dict is None:
            self._aux_dict = Executor._get_dict(
                self._symbol.list_auxiliary_states(), self.aux_arrays)
        return self._aux_dict