Dirichlet character χ759(458,⋅)\chi_{759}(458,\cdot)

• Label: 759.458
• Modulus: $759$
• Conductor: $759$
• Order: $110$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$759$
Conductor:	$759$
Order:	$110$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 759.bf

$\chi_{759}(17,\cdot)$ $\chi_{759}(74,\cdot)$ $\chi_{759}(83,\cdot)$ $\chi_{759}(107,\cdot)$ $\chi_{759}(134,\cdot)$ $\chi_{759}(149,\cdot)$ $\chi_{759}(182,\cdot)$ $\chi_{759}(194,\cdot)$ $\chi_{759}(227,\cdot)$ $\chi_{759}(260,\cdot)$ $\chi_{759}(272,\cdot)$ $\chi_{759}(281,\cdot)$ $\chi_{759}(293,\cdot)$ $\chi_{759}(314,\cdot)$ $\chi_{759}(332,\cdot)$ $\chi_{759}(359,\cdot)$ $\chi_{759}(365,\cdot)$ $\chi_{759}(398,\cdot)$ $\chi_{759}(425,\cdot)$ $\chi_{759}(431,\cdot)$ $\chi_{759}(458,\cdot)$ $\chi_{759}(470,\cdot)$ $\chi_{759}(479,\cdot)$ $\chi_{759}(497,\cdot)$ $\chi_{759}(503,\cdot)$ $\chi_{759}(536,\cdot)$ $\chi_{759}(557,\cdot)$ $\chi_{759}(563,\cdot)$ $\chi_{759}(569,\cdot)$ $\chi_{759}(590,\cdot)$ ...

Related number fields

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

Values on generators

$(254,277,166)$ → $(-1,e\left(\frac{7}{10}\right),e\left(\frac{13}{22}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{ 759 }(458, a)$	$-1$	$1$	$e\left(\frac{21}{55}\right)$	$e\left(\frac{42}{55}\right)$	$e\left(\frac{49}{55}\right)$	$e\left(\frac{7}{55}\right)$	$e\left(\frac{8}{55}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{107}{110}\right)$	$e\left(\frac{28}{55}\right)$	$e\left(\frac{29}{55}\right)$	$e\left(\frac{103}{110}\right)$

Gauss sum

Jacobi sum

Kloosterman sum