Gluing up points of Torus to get a new 2-manifold.

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Lets define Torus as set all pair (z1, z2) where z1,z2 $\in$ $\mathbb{C}$ and |z1| = 1,|z2| = 1.

Now if we glue together
(z1, z2) $\sim$ (-z1, -z2)

What the new 2-manifold look like? My guess is its a non-orientable one,Klein bottle maybe?