Dirichlet character χ759(7,⋅)\chi_{759}(7,\cdot)

• Label: 759.7
• Modulus: $759$
• Conductor: $253$
• Order: $110$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$759$
Conductor:	$253$
Order:	$110$
Real:	no
Primitive:	no, induced from $\chi_{253}(7,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 759.z

$\chi_{759}(7,\cdot)$ $\chi_{759}(19,\cdot)$ $\chi_{759}(28,\cdot)$ $\chi_{759}(40,\cdot)$ $\chi_{759}(61,\cdot)$ $\chi_{759}(79,\cdot)$ $\chi_{759}(106,\cdot)$ $\chi_{759}(112,\cdot)$ $\chi_{759}(145,\cdot)$ $\chi_{759}(172,\cdot)$ $\chi_{759}(178,\cdot)$ $\chi_{759}(205,\cdot)$ $\chi_{759}(217,\cdot)$ $\chi_{759}(226,\cdot)$ $\chi_{759}(244,\cdot)$ $\chi_{759}(250,\cdot)$ $\chi_{759}(283,\cdot)$ $\chi_{759}(304,\cdot)$ $\chi_{759}(310,\cdot)$ $\chi_{759}(316,\cdot)$ $\chi_{759}(337,\cdot)$ $\chi_{759}(343,\cdot)$ $\chi_{759}(382,\cdot)$ $\chi_{759}(424,\cdot)$ $\chi_{759}(442,\cdot)$ $\chi_{759}(448,\cdot)$ $\chi_{759}(457,\cdot)$ $\chi_{759}(475,\cdot)$ $\chi_{759}(481,\cdot)$ $\chi_{759}(490,\cdot)$ ...

Related number fields

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

Values on generators

$(254,277,166)$ → $(1,e\left(\frac{7}{10}\right),e\left(\frac{19}{22}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$13$	$14$	$16$	$17$
$\chi_{ 759 }(7, a)$	$1$	$1$	$e\left(\frac{47}{110}\right)$	$e\left(\frac{47}{55}\right)$	$e\left(\frac{73}{110}\right)$	$e\left(\frac{17}{55}\right)$	$e\left(\frac{31}{110}\right)$	$e\left(\frac{1}{11}\right)$	$e\left(\frac{87}{110}\right)$	$e\left(\frac{81}{110}\right)$	$e\left(\frac{39}{55}\right)$	$e\left(\frac{19}{55}\right)$

Gauss sum

Jacobi sum

Kloosterman sum