In a symbol, if the three angular momenta do not satisfy the triangle conditions (34.2.1), or if the projective quantum numbers do not satisfy (34.2.3), then the symbol is zero. Similarly the symbol (34.4.1) vanishes when the triangle conditions are not satisfied by any of the four symbols in the summation. Such zeros are called trivial zeros. However, the and symbols may vanish for certain combinations of the angular momenta and projective quantum numbers even when the triangle conditions are fulfilled. Such zeros are called nontrivial zeros.
For further information, including examples of nontrivial zeros and extensions to symbols, see Srinivasa Rao and Rajeswari (1993, pp. 133–215, 294–295, 299–310).