Dirichlet character χ128(5,⋅)\chi_{128}(5,\cdot)

• Label: 128.5
• Modulus: $128$
• Conductor: $128$
• Order: $32$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$128$
Conductor:	$128$
Order:	$32$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 128.k

$\chi_{128}(5,\cdot)$ $\chi_{128}(13,\cdot)$ $\chi_{128}(21,\cdot)$ $\chi_{128}(29,\cdot)$ $\chi_{128}(37,\cdot)$ $\chi_{128}(45,\cdot)$ $\chi_{128}(53,\cdot)$ $\chi_{128}(61,\cdot)$ $\chi_{128}(69,\cdot)$ $\chi_{128}(77,\cdot)$ $\chi_{128}(85,\cdot)$ $\chi_{128}(93,\cdot)$ $\chi_{128}(101,\cdot)$ $\chi_{128}(109,\cdot)$ $\chi_{128}(117,\cdot)$ $\chi_{128}(125,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{32})$
Fixed field:	$\Q(\zeta_{128})^+$

Values on generators

$(127,5)$ → $(1,e\left(\frac{1}{32}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 128 }(5, a)$	$1$	$1$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{13}{32}\right)$

Gauss sum

Jacobi sum

Kloosterman sum