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A new hot line list for the main isotopologue of CO$_2$ is presented. Theline list consists of almost 2.5 billion transitions between 3.5 millionrotation-vibration states of CO$_2$ in its ground electronic state, coveringthe wavenumber range 0-20000 cm$^{-1}$ ($\lambda >0.5$ $\mu$m) with the upperand lower energy thresholds of 36 000 cm$^{-1}$ and 16 000 cm$^{-1}$,respectively. The ro-vibrational energies and wavefunctions are computedvariationally using the Ames-2 accurate empirical potential energy surface. Thero-vibrational transition probabilities in the form of Einstein coefficientsare computed using an accurate ab initio dipole moment surface usingvariational program TROVE. A new implementation of TROVE which uses an exactnuclear-motion kinetic energy operator is employed. Comparisons with theexisting hot line lists are presented. The line list should be useful foratmospheric retrievals of exoplanets and cool stars. The UCL-4000 line list isavailable from the CDS and ExoMol databases.

ExoMol line lists -- XXXIX. Ro-vibrational molecular line list for CO$_2$