$x$ |
$\mathrm{E}[x^{0}]$ |
$\mathrm{E}[x^{1}]$ |
$\mathrm{E}[x^{2}]$ |
$\mathrm{E}[x^{3}]$ |
$\mathrm{E}[x^{4}]$ |
$\mathrm{E}[x^{5}]$ |
$\mathrm{E}[x^{6}]$ |
$\mathrm{E}[x^{7}]$ |
$\mathrm{E}[x^{8}]$ |
$\mathrm{E}[x^{9}]$ |
$\mathrm{E}[x^{10}]$ |
$\mathrm{E}[x^{11}]$ |
$\mathrm{E}[x^{12}]$ |
$a_1$ |
$1$ |
$0$ |
$2$ |
$0$ |
$6$ |
$0$ |
$20$ |
$0$ |
$70$ |
$0$ |
$252$ |
$0$ |
$924$ |
Additional information
$\mathrm{U}(1)$ is the Sato-Tate group of an elliptic curve with complex multiplication over any number field that contains the CM field. In all of these cases the Sato-Tate conjecture follows from a classical result of Deuring; see Lemma 2.14 in [arXiv:1604.01256] for a proof.