examples of K-theory groups

$A$	$K_0(A)$	$K_1(A)$
$ℂ$	$\mathbb{Z}$	0
${\mathrm{M}}_n(ℂ)$	$\mathbb{Z}$	0
$ℍ$	$\mathbb{Z}$	0
$𝕂$	$\mathbb{Z}$	0
$𝔹$	0	0
$𝔹/𝕂$	0	$\mathbb{Z}$
$C_0((0,1))$	0	$\mathbb{Z}$
$C_0({ℝ}^{2n})$	$\mathbb{Z}$	0
$C_0({ℝ}^{2n+1})$	0	$\mathbb{Z}$
$C([0,1])$	$\mathbb{Z}$	0
$C({𝕋}^n)$	${\mathbb{Z}}^{2^{n-1}}$	${\mathbb{Z}}^{2^{n-1}}$
$C({𝕊}^{2n})$	${\mathbb{Z}}^2$	0
$C({𝕊}^{2n+1})$	$\mathbb{Z}$	$\mathbb{Z}$
$C(ℂ{\mathrm{P}}^n)$	${\mathbb{Z}}^{n+1}$	0
${𝒪}_n$	$\mathbb{Z}/(n-1)$	0
$A_{\theta }$	${\mathbb{Z}}^2$	${\mathbb{Z}}^2$
$C^{*}(H_3)$	${\mathbb{Z}}^3$	${\mathbb{Z}}^3$

Topological K-theory of some common $C^{*}$-algebras.