\left( a_0 \sigma + b_0 \tilde{\sigma} \right) \left( a_0 \sigma + b_0 \tilde{\sigma} \right) \left( \gamma_0 \sigma + \beta_0 \tilde{\sigma} \right)^n \: = \: q_0, \: \: \: \left(  \gamma_0 \sigma + \beta_0 \tilde{\sigma} \right) \left( \gamma_0 \sigma + \beta_0 \tilde{\sigma} \right) \: = \: q_0,