Dirichlet character χ405(152,⋅)\chi_{405}(152,\cdot)

• Label: 405.152
• Modulus: $405$
• Conductor: $135$
• Order: $36$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$405$
Conductor:	$135$
Order:	$36$
Real:	no
Primitive:	no, induced from $\chi_{135}(122,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 405.r

$\chi_{405}(8,\cdot)$ $\chi_{405}(17,\cdot)$ $\chi_{405}(62,\cdot)$ $\chi_{405}(98,\cdot)$ $\chi_{405}(143,\cdot)$ $\chi_{405}(152,\cdot)$ $\chi_{405}(197,\cdot)$ $\chi_{405}(233,\cdot)$ $\chi_{405}(278,\cdot)$ $\chi_{405}(287,\cdot)$ $\chi_{405}(332,\cdot)$ $\chi_{405}(368,\cdot)$

Related number fields

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

Values on generators

$(326,82)$ → $(e\left(\frac{17}{18}\right),i)$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 405 }(152, a)$	$1$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{5}{6}\right)$

Gauss sum

Jacobi sum

Kloosterman sum