Azimuthal spectra of unstable curvature-driven flute modes in the gas-dynamic trap (GDT) are found to be consistent with theory when including the finite larmor radius (FLR) terms. Growth rates of the modes have been measured for different values of pressure-weighted curvature of the field lines inside the trap and also for different ion pressures changed with auxiliary ion cyclotron heating. A transition from the spectra dominated by the mode of rigid displacement of the plasma column to that where a few modes have approximately the same growth rates was observed.