Dirichlet character χ253(28,⋅)\chi_{253}(28,\cdot)

• Label: 253.28
• Modulus: $253$
• Conductor: $253$
• Order: $110$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$253$
Conductor:	$253$
Order:	$110$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 253.n

$\chi_{253}(7,\cdot)$ $\chi_{253}(17,\cdot)$ $\chi_{253}(19,\cdot)$ $\chi_{253}(28,\cdot)$ $\chi_{253}(30,\cdot)$ $\chi_{253}(40,\cdot)$ $\chi_{253}(51,\cdot)$ $\chi_{253}(57,\cdot)$ $\chi_{253}(61,\cdot)$ $\chi_{253}(63,\cdot)$ $\chi_{253}(74,\cdot)$ $\chi_{253}(79,\cdot)$ $\chi_{253}(83,\cdot)$ $\chi_{253}(84,\cdot)$ $\chi_{253}(90,\cdot)$ $\chi_{253}(106,\cdot)$ $\chi_{253}(107,\cdot)$ $\chi_{253}(112,\cdot)$ $\chi_{253}(129,\cdot)$ $\chi_{253}(134,\cdot)$ $\chi_{253}(145,\cdot)$ $\chi_{253}(149,\cdot)$ $\chi_{253}(171,\cdot)$ $\chi_{253}(172,\cdot)$ $\chi_{253}(178,\cdot)$ $\chi_{253}(182,\cdot)$ $\chi_{253}(189,\cdot)$ $\chi_{253}(194,\cdot)$ $\chi_{253}(195,\cdot)$ $\chi_{253}(204,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{55})$
Fixed field:	Number field defined by a degree 110 polynomial (not computed)

Values on generators

$(24,166)$ → $(e\left(\frac{9}{10}\right),e\left(\frac{1}{22}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 253 }(28, a)$	$1$	$1$	$e\left(\frac{109}{110}\right)$	$e\left(\frac{51}{55}\right)$	$e\left(\frac{54}{55}\right)$	$e\left(\frac{71}{110}\right)$	$e\left(\frac{101}{110}\right)$	$e\left(\frac{9}{55}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{7}{11}\right)$	$e\left(\frac{10}{11}\right)$

Gauss sum

Jacobi sum

Kloosterman sum