Dirichlet character χ269(20,⋅)\chi_{269}(20,\cdot)

• Label: 269.20
• Modulus: $269$
• Conductor: $269$
• Order: $134$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$269$
Conductor:	$269$
Order:	$134$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 269.e

$\chi_{269}(4,\cdot)$ $\chi_{269}(6,\cdot)$ $\chi_{269}(9,\cdot)$ $\chi_{269}(11,\cdot)$ $\chi_{269}(13,\cdot)$ $\chi_{269}(20,\cdot)$ $\chi_{269}(30,\cdot)$ $\chi_{269}(34,\cdot)$ $\chi_{269}(43,\cdot)$ $\chi_{269}(45,\cdot)$ $\chi_{269}(49,\cdot)$ $\chi_{269}(51,\cdot)$ $\chi_{269}(55,\cdot)$ $\chi_{269}(56,\cdot)$ $\chi_{269}(64,\cdot)$ $\chi_{269}(65,\cdot)$ $\chi_{269}(73,\cdot)$ $\chi_{269}(79,\cdot)$ $\chi_{269}(84,\cdot)$ $\chi_{269}(89,\cdot)$ $\chi_{269}(92,\cdot)$ $\chi_{269}(96,\cdot)$ $\chi_{269}(97,\cdot)$ $\chi_{269}(100,\cdot)$ $\chi_{269}(103,\cdot)$ $\chi_{269}(126,\cdot)$ $\chi_{269}(127,\cdot)$ $\chi_{269}(133,\cdot)$ $\chi_{269}(138,\cdot)$ $\chi_{269}(144,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{67})$
Fixed field:	Number field defined by a degree 134 polynomial (not computed)

Values on generators

$2$ → $e\left(\frac{105}{134}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 269 }(20, a)$	$1$	$1$	$e\left(\frac{105}{134}\right)$	$e\left(\frac{55}{134}\right)$	$e\left(\frac{38}{67}\right)$	$e\left(\frac{66}{67}\right)$	$e\left(\frac{13}{67}\right)$	$e\left(\frac{119}{134}\right)$	$e\left(\frac{47}{134}\right)$	$e\left(\frac{55}{67}\right)$	$e\left(\frac{103}{134}\right)$	$e\left(\frac{15}{67}\right)$

Gauss sum

Jacobi sum

Kloosterman sum