Dirichlet character χ269(173,⋅)\chi_{269}(173,\cdot)

• Label: 269.173
• Modulus: $269$
• Conductor: $269$
• Order: $67$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$269$
Conductor:	$269$
Order:	$67$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 269.d

$\chi_{269}(5,\cdot)$ $\chi_{269}(14,\cdot)$ $\chi_{269}(16,\cdot)$ $\chi_{269}(21,\cdot)$ $\chi_{269}(23,\cdot)$ $\chi_{269}(24,\cdot)$ $\chi_{269}(25,\cdot)$ $\chi_{269}(36,\cdot)$ $\chi_{269}(37,\cdot)$ $\chi_{269}(38,\cdot)$ $\chi_{269}(41,\cdot)$ $\chi_{269}(44,\cdot)$ $\chi_{269}(47,\cdot)$ $\chi_{269}(52,\cdot)$ $\chi_{269}(53,\cdot)$ $\chi_{269}(54,\cdot)$ $\chi_{269}(57,\cdot)$ $\chi_{269}(58,\cdot)$ $\chi_{269}(61,\cdot)$ $\chi_{269}(62,\cdot)$ $\chi_{269}(66,\cdot)$ $\chi_{269}(67,\cdot)$ $\chi_{269}(70,\cdot)$ $\chi_{269}(78,\cdot)$ $\chi_{269}(80,\cdot)$ $\chi_{269}(81,\cdot)$ $\chi_{269}(87,\cdot)$ $\chi_{269}(93,\cdot)$ $\chi_{269}(99,\cdot)$ $\chi_{269}(105,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{67})$
Fixed field:	Number field defined by a degree 67 polynomial

Values on generators

$2$ → $e\left(\frac{62}{67}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 269 }(173, a)$	$1$	$1$	$e\left(\frac{62}{67}\right)$	$e\left(\frac{58}{67}\right)$	$e\left(\frac{57}{67}\right)$	$e\left(\frac{32}{67}\right)$	$e\left(\frac{53}{67}\right)$	$e\left(\frac{39}{67}\right)$	$e\left(\frac{52}{67}\right)$	$e\left(\frac{49}{67}\right)$	$e\left(\frac{27}{67}\right)$	$e\left(\frac{56}{67}\right)$

Gauss sum

Jacobi sum

Kloosterman sum