Dirichlet character χ629(13,⋅)\chi_{629}(13,\cdot)

• Label: 629.13
• Modulus: $629$
• Conductor: $629$
• Order: $36$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$629$
Conductor:	$629$
Order:	$36$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 629.bp

$\chi_{629}(13,\cdot)$ $\chi_{629}(55,\cdot)$ $\chi_{629}(89,\cdot)$ $\chi_{629}(106,\cdot)$ $\chi_{629}(183,\cdot)$ $\chi_{629}(242,\cdot)$ $\chi_{629}(387,\cdot)$ $\chi_{629}(446,\cdot)$ $\chi_{629}(523,\cdot)$ $\chi_{629}(540,\cdot)$ $\chi_{629}(574,\cdot)$ $\chi_{629}(616,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	36.0.12858230878574949858207932230482249727234181545281621536549998606426152894209663387757389.1

Values on generators

$(445,409)$ → $(i,e\left(\frac{11}{36}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 629 }(13, a)$	$-1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{5}{18}\right)$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$

Gauss sum

Jacobi sum

Kloosterman sum