Dirichlet character χ675(317,⋅)\chi_{675}(317,\cdot)

• Label: 675.317
• Modulus: $675$
• Conductor: $675$
• Order: $180$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$675$
Conductor:	$675$
Order:	$180$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 675.bi

$\chi_{675}(2,\cdot)$ $\chi_{675}(23,\cdot)$ $\chi_{675}(38,\cdot)$ $\chi_{675}(47,\cdot)$ $\chi_{675}(77,\cdot)$ $\chi_{675}(83,\cdot)$ $\chi_{675}(92,\cdot)$ $\chi_{675}(113,\cdot)$ $\chi_{675}(122,\cdot)$ $\chi_{675}(128,\cdot)$ $\chi_{675}(137,\cdot)$ $\chi_{675}(158,\cdot)$ $\chi_{675}(167,\cdot)$ $\chi_{675}(173,\cdot)$ $\chi_{675}(203,\cdot)$ $\chi_{675}(212,\cdot)$ $\chi_{675}(227,\cdot)$ $\chi_{675}(248,\cdot)$ $\chi_{675}(263,\cdot)$ $\chi_{675}(272,\cdot)$ $\chi_{675}(302,\cdot)$ $\chi_{675}(308,\cdot)$ $\chi_{675}(317,\cdot)$ $\chi_{675}(338,\cdot)$ $\chi_{675}(347,\cdot)$ $\chi_{675}(353,\cdot)$ $\chi_{675}(362,\cdot)$ $\chi_{675}(383,\cdot)$ $\chi_{675}(392,\cdot)$ $\chi_{675}(398,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{180})$
Fixed field:	Number field defined by a degree 180 polynomial (not computed)

Values on generators

$(326,352)$ → $(e\left(\frac{7}{18}\right),e\left(\frac{13}{20}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 675 }(317, a)$	$1$	$1$	$e\left(\frac{7}{180}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{41}{90}\right)$	$e\left(\frac{83}{180}\right)$	$e\left(\frac{23}{45}\right)$	$e\left(\frac{7}{45}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{11}{30}\right)$

Gauss sum

Jacobi sum

Kloosterman sum