Dirichlet character χ135(23,⋅)\chi_{135}(23,\cdot)

• Label: 135.23
• Modulus: $135$
• Conductor: $135$
• Order: $36$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$135$
Conductor:	$135$
Order:	$36$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 135.q

$\chi_{135}(2,\cdot)$ $\chi_{135}(23,\cdot)$ $\chi_{135}(32,\cdot)$ $\chi_{135}(38,\cdot)$ $\chi_{135}(47,\cdot)$ $\chi_{135}(68,\cdot)$ $\chi_{135}(77,\cdot)$ $\chi_{135}(83,\cdot)$ $\chi_{135}(92,\cdot)$ $\chi_{135}(113,\cdot)$ $\chi_{135}(122,\cdot)$ $\chi_{135}(128,\cdot)$

Related number fields

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

Values on generators

$(56,82)$ → $(e\left(\frac{11}{18}\right),-i)$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 135 }(23, a)$	$1$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$

Gauss sum

Jacobi sum

Kloosterman sum