Dirichlet character χ629(354,⋅)\chi_{629}(354,\cdot)

• Label: 629.354
• Modulus: $629$
• Conductor: $629$
• Order: $144$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$629$
Conductor:	$629$
Order:	$144$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 629.cb

$\chi_{629}(3,\cdot)$ $\chi_{629}(28,\cdot)$ $\chi_{629}(40,\cdot)$ $\chi_{629}(41,\cdot)$ $\chi_{629}(58,\cdot)$ $\chi_{629}(62,\cdot)$ $\chi_{629}(65,\cdot)$ $\chi_{629}(78,\cdot)$ $\chi_{629}(95,\cdot)$ $\chi_{629}(99,\cdot)$ $\chi_{629}(114,\cdot)$ $\chi_{629}(139,\cdot)$ $\chi_{629}(141,\cdot)$ $\chi_{629}(173,\cdot)$ $\chi_{629}(176,\cdot)$ $\chi_{629}(210,\cdot)$ $\chi_{629}(215,\cdot)$ $\chi_{629}(226,\cdot)$ $\chi_{629}(243,\cdot)$ $\chi_{629}(250,\cdot)$ $\chi_{629}(252,\cdot)$ $\chi_{629}(262,\cdot)$ $\chi_{629}(284,\cdot)$ $\chi_{629}(299,\cdot)$ $\chi_{629}(300,\cdot)$ $\chi_{629}(317,\cdot)$ $\chi_{629}(326,\cdot)$ $\chi_{629}(337,\cdot)$ $\chi_{629}(354,\cdot)$ $\chi_{629}(363,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{144})$
Fixed field:	Number field defined by a degree 144 polynomial (not computed)

Values on generators

$(445,409)$ → $(e\left(\frac{9}{16}\right),e\left(\frac{11}{18}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 629 }(354, a)$	$-1$	$1$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{13}{48}\right)$

Gauss sum

Jacobi sum

Kloosterman sum