Dirichlet character χ512(189,⋅)\chi_{512}(189,\cdot)

• Label: 512.189
• Modulus: $512$
• Conductor: $512$
• Order: $128$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$512$
Conductor:	$512$
Order:	$128$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 512.o

$\chi_{512}(5,\cdot)$ $\chi_{512}(13,\cdot)$ $\chi_{512}(21,\cdot)$ $\chi_{512}(29,\cdot)$ $\chi_{512}(37,\cdot)$ $\chi_{512}(45,\cdot)$ $\chi_{512}(53,\cdot)$ $\chi_{512}(61,\cdot)$ $\chi_{512}(69,\cdot)$ $\chi_{512}(77,\cdot)$ $\chi_{512}(85,\cdot)$ $\chi_{512}(93,\cdot)$ $\chi_{512}(101,\cdot)$ $\chi_{512}(109,\cdot)$ $\chi_{512}(117,\cdot)$ $\chi_{512}(125,\cdot)$ $\chi_{512}(133,\cdot)$ $\chi_{512}(141,\cdot)$ $\chi_{512}(149,\cdot)$ $\chi_{512}(157,\cdot)$ $\chi_{512}(165,\cdot)$ $\chi_{512}(173,\cdot)$ $\chi_{512}(181,\cdot)$ $\chi_{512}(189,\cdot)$ $\chi_{512}(197,\cdot)$ $\chi_{512}(205,\cdot)$ $\chi_{512}(213,\cdot)$ $\chi_{512}(221,\cdot)$ $\chi_{512}(229,\cdot)$ $\chi_{512}(237,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{128})$
Fixed field:	Number field defined by a degree 128 polynomial (not computed)

Values on generators

$(511,5)$ → $(1,e\left(\frac{51}{128}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 512 }(189, a)$	$1$	$1$	$e\left(\frac{121}{128}\right)$	$e\left(\frac{51}{128}\right)$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{111}{128}\right)$	$e\left(\frac{29}{128}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{21}{128}\right)$	$e\left(\frac{55}{128}\right)$

Gauss sum

Jacobi sum

Kloosterman sum