[math] \newcommand{\mathds}{\mathbb}[/math]

Work out all the details for the truncated character formula for [math]H_N^s[/math],

[[math]] \chi_t\sim b^s_t [[/math]]

where [math]b_t^s=p_{t\varepsilon_s}[/math], with [math]\varepsilon_s[/math] being the uniform measure on the [math]s[/math]-th roots of unity.