def pauli_tuple(self, pauli: Pauli) -> tuple[Pauli, bool]:
        """Returns a tuple of a Pauli operator and a boolean.

        The pauli is the operator of the transform and the boolean
        determines whether the operator should be flipped.  For instance,
        it is True if the coefficient is -1, and False if the coefficient
        is 1.
        """
        x_to = self._clifford_tableau.destabilizers()[0]
        z_to = self._clifford_tableau.stabilizers()[0]
        if pauli == pauli_gates.X:
            to = x_to
        elif pauli == pauli_gates.Z:
            to = z_to
        else:
            to = x_to * z_to  # Y = iXZ
            to._coefficient *= 1j
        # pauli_mask returns a value between 0 and 4 for [I, X, Y, Z].
        to_gate = Pauli._XYZ[to.pauli_mask[0] - 1]
        return (to_gate, bool(to.coefficient != 1.0))
Returns a tuple of a Pauli operator and a boolean.

        The pauli is the operator of the transform and the boolean
        determines whether the operator should be flipped.  For instance,
        it is True if the coefficient is -1, and False if the coefficient
        is 1.
        
cirq-core/cirq/ops/clifford_gate.py