  This study delves into the realm of chaotic dynamics derived from Dirichlet L
functions, drawing inspiration from Yitang Zhang's groundbreaking work on
Landau Siegel zeros. The dynamic behavior reveals a profound chaos,
corroborated by the calculated Lyapunov exponents and entropy, which attest to
the system's inherent unpredictability. The examination of stability further
uncovers the instability of fixed points. Most notably, these findings unveil a
compelling connection between the studied dynamics and the intricate
distribution of zeros, thereby offering indirect support for Zhang's
groundbreaking theorem concerning Landau Siegel zeros.
