Dirichlet character χ675(518,⋅)\chi_{675}(518,\cdot)

• Label: 675.518
• Modulus: $675$
• Conductor: $135$
• Order: $36$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$675$
Conductor:	$135$
Order:	$36$
Real:	no
Primitive:	no, induced from $\chi_{135}(113,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 675.ba

$\chi_{675}(32,\cdot)$ $\chi_{675}(68,\cdot)$ $\chi_{675}(182,\cdot)$ $\chi_{675}(218,\cdot)$ $\chi_{675}(257,\cdot)$ $\chi_{675}(293,\cdot)$ $\chi_{675}(407,\cdot)$ $\chi_{675}(443,\cdot)$ $\chi_{675}(482,\cdot)$ $\chi_{675}(518,\cdot)$ $\chi_{675}(632,\cdot)$ $\chi_{675}(668,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	$\Q(\zeta_{135})^+$

Values on generators

$(326,352)$ → $(e\left(\frac{5}{18}\right),-i)$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 675 }(518, a)$	$1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

Gauss sum

Jacobi sum

Kloosterman sum