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We present a large ${\sim 30" \times 30"}$ spectroscopic survey of the Galactic Center using the SINFONI IFU at the VLT. Combining observations of the last two decades we compile spectra of over $2800$ stars. Using the Bracket-$\gamma$ absorption lines we identify $195$ young stars, extending the list of known young stars by $79$. In order to explore the angular momentum distribution of the young stars, we introduce an isotropic cluster prior. This prior reproduces an isotropic cluster in a mathematically exact way, which we test through numerical simulations. We calculate the posterior angular momentum space as function of projected separation from Sgr~A*. We find that the observed young star distribution is substantially different from an isotropic cluster. We identify the previously reported feature of the clockwise disk and find that its angular momentum changes as function of separation from the black hole, and thus confirm a warp of the clockwise disk ($p \sim 99.2\%$). At large separations, we discover three prominent overdensities of angular momentum. One overdensity has been reported previously, the counter-clockwise disk. The other two are new. Determining the likely members of these structures, we find that as many as $75\%$ of stars can be associated with one of these features. Stars belonging to the warped clockwise-disk show a top heavy K-band luminosity function, while stars belonging to the larger separation features do not. Our observations are in good agreement with the predictions of simulations of in-situ star formation, and argue for common formation of these structures., Comment: Accepted for Publication in APJL