Dirichlet character χ253(36,⋅)\chi_{253}(36,\cdot)

• Label: 253.36
• Modulus: $253$
• Conductor: $253$
• Order: $55$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$253$
Conductor:	$253$
Order:	$55$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 253.m

$\chi_{253}(3,\cdot)$ $\chi_{253}(4,\cdot)$ $\chi_{253}(9,\cdot)$ $\chi_{253}(16,\cdot)$ $\chi_{253}(25,\cdot)$ $\chi_{253}(26,\cdot)$ $\chi_{253}(27,\cdot)$ $\chi_{253}(31,\cdot)$ $\chi_{253}(36,\cdot)$ $\chi_{253}(48,\cdot)$ $\chi_{253}(49,\cdot)$ $\chi_{253}(58,\cdot)$ $\chi_{253}(59,\cdot)$ $\chi_{253}(64,\cdot)$ $\chi_{253}(71,\cdot)$ $\chi_{253}(75,\cdot)$ $\chi_{253}(81,\cdot)$ $\chi_{253}(82,\cdot)$ $\chi_{253}(104,\cdot)$ $\chi_{253}(108,\cdot)$ $\chi_{253}(119,\cdot)$ $\chi_{253}(124,\cdot)$ $\chi_{253}(141,\cdot)$ $\chi_{253}(146,\cdot)$ $\chi_{253}(147,\cdot)$ $\chi_{253}(163,\cdot)$ $\chi_{253}(169,\cdot)$ $\chi_{253}(170,\cdot)$ $\chi_{253}(174,\cdot)$ $\chi_{253}(179,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 55 polynomial

Values on generators

$(24,166)$ → $(e\left(\frac{4}{5}\right),e\left(\frac{7}{11}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 253 }(36, a)$	$1$	$1$	$e\left(\frac{4}{55}\right)$	$e\left(\frac{32}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{46}{55}\right)$	$e\left(\frac{36}{55}\right)$	$e\left(\frac{38}{55}\right)$	$e\left(\frac{12}{55}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{10}{11}\right)$	$e\left(\frac{8}{11}\right)$

Gauss sum

Jacobi sum

Kloosterman sum