Dirichlet character χ759(58,⋅)\chi_{759}(58,\cdot)

• Label: 759.58
• Modulus: $759$
• Conductor: $253$
• Order: $55$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$759$
Conductor:	$253$
Order:	$55$
Real:	no
Primitive:	no, induced from $\chi_{253}(58,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 759.y

$\chi_{759}(4,\cdot)$ $\chi_{759}(16,\cdot)$ $\chi_{759}(25,\cdot)$ $\chi_{759}(31,\cdot)$ $\chi_{759}(49,\cdot)$ $\chi_{759}(58,\cdot)$ $\chi_{759}(64,\cdot)$ $\chi_{759}(82,\cdot)$ $\chi_{759}(124,\cdot)$ $\chi_{759}(163,\cdot)$ $\chi_{759}(169,\cdot)$ $\chi_{759}(190,\cdot)$ $\chi_{759}(196,\cdot)$ $\chi_{759}(202,\cdot)$ $\chi_{759}(223,\cdot)$ $\chi_{759}(256,\cdot)$ $\chi_{759}(262,\cdot)$ $\chi_{759}(280,\cdot)$ $\chi_{759}(289,\cdot)$ $\chi_{759}(301,\cdot)$ $\chi_{759}(328,\cdot)$ $\chi_{759}(334,\cdot)$ $\chi_{759}(361,\cdot)$ $\chi_{759}(394,\cdot)$ $\chi_{759}(400,\cdot)$ $\chi_{759}(427,\cdot)$ $\chi_{759}(445,\cdot)$ $\chi_{759}(466,\cdot)$ $\chi_{759}(478,\cdot)$ $\chi_{759}(487,\cdot)$ ...

Related number fields

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

Values on generators

$(254,277,166)$ → $(1,e\left(\frac{4}{5}\right),e\left(\frac{10}{11}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{ 759 }(58, a)$	$1$	$1$	$e\left(\frac{34}{55}\right)$	$e\left(\frac{13}{55}\right)$	$e\left(\frac{6}{55}\right)$	$e\left(\frac{48}{55}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{8}{11}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{27}{55}\right)$	$e\left(\frac{26}{55}\right)$	$e\left(\frac{31}{55}\right)$

Gauss sum

Jacobi sum

Kloosterman sum