Sato-Tate group μ(608)\mu(608) of weight 0 and degree 1

• Label: 0.1.608
• Name: $\mu(608)$
• Weight: $0$
• Degree: $1$
• Real dimension: $0$
• Components: $608$
• Contained in: $\mathrm{O}(1)$
• Identity component: $\mathrm{SO}(1)$
• Component group: $C_{608}$

Invariants

Weight:	$0$
Degree:	$1$
$\mathbb{R}$-dimension:	$0$
Components:	$608$
Contained in:	$\mathrm{O}(1)$
Rational:	yes

Identity component

Name:	$\mathrm{SO}(1)$
$\mathbb{R}$-dimension:	$0$
Description:	$\textsf{trivial}$

Component group

Name:	$C_{608}$
Order:	$608$
Abelian:	yes
Generators:	$\begin{bmatrix}\zeta_{608}\end{bmatrix}$

Subgroups and supergroups

Maximal subgroups:	$\mu(304)$, $\mu(32)$
Minimal supergroups:	$\mu(1216)$, $\mu(1824)$, $\mu(3040)$, $\cdots$

Moment sequences

$x$	$\mathrm{E}[x^{0}]$	$\mathrm{E}[x^{1}]$	$\mathrm{E}[x^{2}]$	$\mathrm{E}[x^{3}]$	$\mathrm{E}[x^{4}]$	$\mathrm{E}[x^{5}]$	$\mathrm{E}[x^{6}]$	$\mathrm{E}[x^{7}]$	$\mathrm{E}[x^{8}]$	$\mathrm{E}[x^{9}]$	$\mathrm{E}[x^{10}]$	$\mathrm{E}[x^{11}]$	$\mathrm{E}[x^{12}]$
$a_1$	$1$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$

Event probabilities

$\mathrm{Pr}[a_1=1]=1/608$