In this paper, we give an explicit description of the good, semi-good, and bad elements in
T×C*. These three concepts were introduced by Xi for proving the
Deligne&
ndash;Langlands conjecture for complex
affine Hecke algebras when the order of the nonzero complex parameter
q is not too small. First, we define the root graph of a root system and the degenerate paths associated with an element (
s,
q)
T×C*. Then we establish a criterion for (
s,
q) being good in terms of the non-existence of the degenerate paths associated with (
s,
q) in the corresponding root graph. Finally, we distinguish the bad elements from the semi-good ones by the vanishing of the Poincaré polynomial at
q.