  We measure the thermodynamic magnetization of a low-disordered, strongly
correlated two-dimensional electron system in silicon in perpendicular magnetic
fields. A new, parameter-free method is used to directly determine the spectrum
characteristics (Lande g-factor and the cyclotron mass) when the Fermi level
lies outside the spectral gaps and the inter-level interactions between
quasiparticles are avoided. Intra-level interactions are found to strongly
modify the magnetization, without affecting the determined g* and m*.
