1. INTRODUCTION  
2.2. ASPECS Sample  
2.3. Very Large Array Observations (VLASPECS)  
2.4. Multi-wavelength data & SED fitting  
3. METHODS  
3.1. Spectral line analysis  
3.2. Deriving line luminosities and molecular gas masses  
4. RESULTS  
4.1. Observed emission lines from CO and [C i]  
5. CO EXCITATION  
5.1. Individual sources  
5.2. Stacked line fluxes  
5.3. LVG modeling  
5.4. Dust continuum versus low-J CO  
6. ATOMIC CARBON  
6.1. Atomic carbon abundances  
6.2. PDR modeling  
7. DISCUSSION  
7.1. Modest excitation in mid-J lines at $z=1.0-1.6$  
7.2. Increasing excitation with redshift  
7.3. The low-J excitation  
7.4. Broader implications of the flux-limited survey  
7.5. Implications for the cosmic molecular gas density  
8. SUMMARY AND CONCLUSIONS