  In this paper we study the dimension spectrum of general conformal graph
directed Markov systems modeled by countable state symbolic subshifts of finite
type. We perform a comprehensive study of the dimension spectrum addressing
questions regarding its size and topological structure. As a corollary we
obtain that the dimension spectrum of infinite conformal iterated function
systems is compact and perfect. On the way we revisit the role of the parameter
$\theta$ in graph directed Markov systems and we show that new phenomena arise.
  We also establish topological pressure estimates for subsystems in the
abstract setting of symbolic dynamics with countable alphabets. These estimates
play a crucial role in our proofs regarding the dimension spectrum, and they
allow us to study Hausdorff dimension asymptotics for subsystems.
  Finally we narrow our focus to the dimension spectrum of conformal iterated
function systems and we prove, among other things, that the iterated function
system resulting from the complex continued fractions algorithm has full
dimension spectrum. We thus give a positive answer to the Texan conjecture for
complex continued fractions.
