Dirichlet character χ288(155,⋅)\chi_{288}(155,\cdot)

• Label: 288.155
• Modulus: $288$
• Conductor: $288$
• Order: $24$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$288$
Conductor:	$288$
Order:	$24$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 288.bf

$\chi_{288}(11,\cdot)$ $\chi_{288}(59,\cdot)$ $\chi_{288}(83,\cdot)$ $\chi_{288}(131,\cdot)$ $\chi_{288}(155,\cdot)$ $\chi_{288}(203,\cdot)$ $\chi_{288}(227,\cdot)$ $\chi_{288}(275,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{24})$
Fixed field:	24.24.1486465269728735333725176976133731985582456832.1

Values on generators

$(127,37,65)$ → $(-1,e\left(\frac{1}{8}\right),e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{ 288 }(155, a)$	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{5}{24}\right)$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{6}\right)$

Gauss sum

Jacobi sum

Kloosterman sum