Dirichlet character χ405(68,⋅)\chi_{405}(68,\cdot)

• Label: 405.68
• Modulus: $405$
• Conductor: $405$
• Order: $108$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 405.x

$\chi_{405}(2,\cdot)$ $\chi_{405}(23,\cdot)$ $\chi_{405}(32,\cdot)$ $\chi_{405}(38,\cdot)$ $\chi_{405}(47,\cdot)$ $\chi_{405}(68,\cdot)$ $\chi_{405}(77,\cdot)$ $\chi_{405}(83,\cdot)$ $\chi_{405}(92,\cdot)$ $\chi_{405}(113,\cdot)$ $\chi_{405}(122,\cdot)$ $\chi_{405}(128,\cdot)$ $\chi_{405}(137,\cdot)$ $\chi_{405}(158,\cdot)$ $\chi_{405}(167,\cdot)$ $\chi_{405}(173,\cdot)$ $\chi_{405}(182,\cdot)$ $\chi_{405}(203,\cdot)$ $\chi_{405}(212,\cdot)$ $\chi_{405}(218,\cdot)$ $\chi_{405}(227,\cdot)$ $\chi_{405}(248,\cdot)$ $\chi_{405}(257,\cdot)$ $\chi_{405}(263,\cdot)$ $\chi_{405}(272,\cdot)$ $\chi_{405}(293,\cdot)$ $\chi_{405}(302,\cdot)$ $\chi_{405}(308,\cdot)$ $\chi_{405}(317,\cdot)$ $\chi_{405}(338,\cdot)$ ...

Related number fields

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

Values on generators

$(326,82)$ → $(e\left(\frac{35}{54}\right),-i)$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 405 }(68, a)$	$1$	$1$	$e\left(\frac{43}{108}\right)$	$e\left(\frac{43}{54}\right)$	$e\left(\frac{13}{108}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{23}{54}\right)$	$e\left(\frac{47}{108}\right)$	$e\left(\frac{14}{27}\right)$	$e\left(\frac{16}{27}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{18}\right)$

Gauss sum

Jacobi sum

Kloosterman sum