Dirichlet character χ945(857,⋅)\chi_{945}(857,\cdot)

• Label: 945.857
• Modulus: $945$
• Conductor: $945$
• Order: $36$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$945$
Conductor:	$945$
Order:	$36$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 945.dq

$\chi_{945}(38,\cdot)$ $\chi_{945}(68,\cdot)$ $\chi_{945}(227,\cdot)$ $\chi_{945}(257,\cdot)$ $\chi_{945}(353,\cdot)$ $\chi_{945}(383,\cdot)$ $\chi_{945}(542,\cdot)$ $\chi_{945}(572,\cdot)$ $\chi_{945}(668,\cdot)$ $\chi_{945}(698,\cdot)$ $\chi_{945}(857,\cdot)$ $\chi_{945}(887,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	36.0.1465697146251004474650413649141163426679210854529430772252466557978101074695587158203125.1

Values on generators

$(596,757,136)$ → $(e\left(\frac{7}{18}\right),i,e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$23$
$\chi_{ 945 }(857, a)$	$-1$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{8}{9}\right)$	$i$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{13}{36}\right)$

Gauss sum

Jacobi sum

Kloosterman sum