Dirichlet character χ405(58,⋅)\chi_{405}(58,\cdot)

• Label: 405.58
• Modulus: $405$
• Conductor: $405$
• Order: $108$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$405$
Conductor:	$405$
Order:	$108$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 405.w

$\chi_{405}(7,\cdot)$ $\chi_{405}(13,\cdot)$ $\chi_{405}(22,\cdot)$ $\chi_{405}(43,\cdot)$ $\chi_{405}(52,\cdot)$ $\chi_{405}(58,\cdot)$ $\chi_{405}(67,\cdot)$ $\chi_{405}(88,\cdot)$ $\chi_{405}(97,\cdot)$ $\chi_{405}(103,\cdot)$ $\chi_{405}(112,\cdot)$ $\chi_{405}(133,\cdot)$ $\chi_{405}(142,\cdot)$ $\chi_{405}(148,\cdot)$ $\chi_{405}(157,\cdot)$ $\chi_{405}(178,\cdot)$ $\chi_{405}(187,\cdot)$ $\chi_{405}(193,\cdot)$ $\chi_{405}(202,\cdot)$ $\chi_{405}(223,\cdot)$ $\chi_{405}(232,\cdot)$ $\chi_{405}(238,\cdot)$ $\chi_{405}(247,\cdot)$ $\chi_{405}(268,\cdot)$ $\chi_{405}(277,\cdot)$ $\chi_{405}(283,\cdot)$ $\chi_{405}(292,\cdot)$ $\chi_{405}(313,\cdot)$ $\chi_{405}(322,\cdot)$ $\chi_{405}(328,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{108})$
Fixed field:	Number field defined by a degree 108 polynomial (not computed)

Values on generators

$(326,82)$ → $(e\left(\frac{19}{27}\right),-i)$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 405 }(58, a)$	$-1$	$1$	$e\left(\frac{49}{108}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{1}{108}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{4}{27}\right)$	$e\left(\frac{95}{108}\right)$	$e\left(\frac{25}{54}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{18}\right)$

Gauss sum

Jacobi sum

Kloosterman sum