| List I -complex | List II-CFSE | ||
| A | [Cu(NH3)6]2+ | I | -6.0 |
| B | [Ti(H2O)6]3+ | II | -2.0 |
| C | [Fe(CN)6]3- | III | -1.2 |
| D | [NiF6]4- | IV | -0.4 |
Choose the correct answer from the options given below:
Calculate the potential for half-cell containing 0.01 M K\(_2\)Cr\(_2\)O\(_7\)(aq), 0.01 M Cr\(^{3+}\)(aq), and 1.0 x 10\(^{-4}\) M H\(^+\)(aq).

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.