Dirichlet character χ269(27,⋅)\chi_{269}(27,\cdot)

• Label: 269.27
• Modulus: $269$
• Conductor: $269$
• Order: $268$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$269$
Conductor:	$269$
Order:	$268$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 269.f

$\chi_{269}(2,\cdot)$ $\chi_{269}(3,\cdot)$ $\chi_{269}(7,\cdot)$ $\chi_{269}(8,\cdot)$ $\chi_{269}(10,\cdot)$ $\chi_{269}(12,\cdot)$ $\chi_{269}(15,\cdot)$ $\chi_{269}(17,\cdot)$ $\chi_{269}(18,\cdot)$ $\chi_{269}(19,\cdot)$ $\chi_{269}(22,\cdot)$ $\chi_{269}(26,\cdot)$ $\chi_{269}(27,\cdot)$ $\chi_{269}(28,\cdot)$ $\chi_{269}(29,\cdot)$ $\chi_{269}(31,\cdot)$ $\chi_{269}(32,\cdot)$ $\chi_{269}(33,\cdot)$ $\chi_{269}(35,\cdot)$ $\chi_{269}(39,\cdot)$ $\chi_{269}(40,\cdot)$ $\chi_{269}(42,\cdot)$ $\chi_{269}(46,\cdot)$ $\chi_{269}(48,\cdot)$ $\chi_{269}(50,\cdot)$ $\chi_{269}(59,\cdot)$ $\chi_{269}(60,\cdot)$ $\chi_{269}(63,\cdot)$ $\chi_{269}(68,\cdot)$ $\chi_{269}(69,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{268})$
Fixed field:	Number field defined by a degree 268 polynomial (not computed)

Values on generators

$2$ → $e\left(\frac{59}{268}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 269 }(27, a)$	$-1$	$1$	$e\left(\frac{59}{268}\right)$	$e\left(\frac{267}{268}\right)$	$e\left(\frac{59}{134}\right)$	$e\left(\frac{53}{67}\right)$	$e\left(\frac{29}{134}\right)$	$e\left(\frac{49}{268}\right)$	$e\left(\frac{177}{268}\right)$	$e\left(\frac{133}{134}\right)$	$e\left(\frac{3}{268}\right)$	$e\left(\frac{85}{134}\right)$

Gauss sum

Jacobi sum

Kloosterman sum