Dirichlet character χ288(277,⋅)\chi_{288}(277,\cdot)

• Label: 288.277
• 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.bc

$\chi_{288}(13,\cdot)$ $\chi_{288}(61,\cdot)$ $\chi_{288}(85,\cdot)$ $\chi_{288}(133,\cdot)$ $\chi_{288}(157,\cdot)$ $\chi_{288}(205,\cdot)$ $\chi_{288}(229,\cdot)$ $\chi_{288}(277,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{24})$
Fixed field:	24.24.18351423083070806589199715754737431920771072.1

Values on generators

$(127,37,65)$ → $(1,e\left(\frac{5}{8}\right),e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{ 288 }(277, a)$	$1$	$1$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{17}{24}\right)$	$-1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum