Let the complex numbers $\alpha$ and $\frac { 1 } { \alpha }$ lie on the circles $\mathrm { z } - \mathrm { z } _ { 0 } { } ^ { 2 } = 4$ and $\mathrm { z } - \mathrm { z } _ { 0 } { } ^ { 2 } = 16$ respectively, where $\mathrm { z } _ { 0 } = 1 + \mathrm { i }$. Then, the value of $100 | \alpha | ^ { 2 }$ is $\_\_\_\_$ .