From perspective of observer at rest

$t_{total}$

$x_{total}$

$y_{total}$

$z_{total}$

The moving frame to forward

$t^{\prime }$

$x^{\prime }$

$\frac{y^{\prime }}{\gamma }$

$\frac{z^{\prime }}{\gamma }$

The moving frame to backward

$t^{\prime }\left(\gamma -1\right)$

$x^{\prime }\left(\gamma -1\right)$

$y^{\prime }\left(\gamma -1\right)$

$z^{\prime }\left(\gamma -1\right)$

The final result

$t^{\prime }\left(\gamma \right)$

$\frac{x^{\prime }}{\gamma }$

$y^{\prime }$

$z^{\prime }$