Dirichlet character χ265(224,⋅)\chi_{265}(224,\cdot)

• Label: 265.224
• Modulus: $265$
• Conductor: $265$
• Order: $52$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$265$
Conductor:	$265$
Order:	$52$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 265.r

$\chi_{265}(14,\cdot)$ $\chi_{265}(19,\cdot)$ $\chi_{265}(34,\cdot)$ $\chi_{265}(39,\cdot)$ $\chi_{265}(74,\cdot)$ $\chi_{265}(79,\cdot)$ $\chi_{265}(84,\cdot)$ $\chi_{265}(94,\cdot)$ $\chi_{265}(104,\cdot)$ $\chi_{265}(109,\cdot)$ $\chi_{265}(114,\cdot)$ $\chi_{265}(124,\cdot)$ $\chi_{265}(139,\cdot)$ $\chi_{265}(154,\cdot)$ $\chi_{265}(164,\cdot)$ $\chi_{265}(179,\cdot)$ $\chi_{265}(194,\cdot)$ $\chi_{265}(204,\cdot)$ $\chi_{265}(209,\cdot)$ $\chi_{265}(214,\cdot)$ $\chi_{265}(224,\cdot)$ $\chi_{265}(234,\cdot)$ $\chi_{265}(239,\cdot)$ $\chi_{265}(244,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Values on generators

$(107,161)$ → $(-1,e\left(\frac{19}{52}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 265 }(224, a)$	$-1$	$1$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{37}{52}\right)$	$e\left(\frac{19}{26}\right)$	$e\left(\frac{15}{26}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{11}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{23}{52}\right)$	$e\left(\frac{7}{26}\right)$

Gauss sum

Jacobi sum

Kloosterman sum