The low multipoles should converge as long as P(k) doesn't diverge too badly towards zero, but of course default accuracy settings assume nearly scale invariant, so you may need to explore settings. If your P(k) does diverge, then obviously not surprising that you get strange behaviour at low L (and you probably need to then calculate something else, like the C_l conditional on the CMB monopole to remove locally-unobservable dependence on superhorizon modes).
Statistics: Posted by Antony Lewis — December 13 2024