Dirichlet character χ405(31,⋅)\chi_{405}(31,\cdot)

• Label: 405.31
• Modulus: $405$
• Conductor: $81$
• Order: $27$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$405$
Conductor:	$81$
Order:	$27$
Real:	no
Primitive:	no, induced from $\chi_{81}(31,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 405.q

$\chi_{405}(16,\cdot)$ $\chi_{405}(31,\cdot)$ $\chi_{405}(61,\cdot)$ $\chi_{405}(76,\cdot)$ $\chi_{405}(106,\cdot)$ $\chi_{405}(121,\cdot)$ $\chi_{405}(151,\cdot)$ $\chi_{405}(166,\cdot)$ $\chi_{405}(196,\cdot)$ $\chi_{405}(211,\cdot)$ $\chi_{405}(241,\cdot)$ $\chi_{405}(256,\cdot)$ $\chi_{405}(286,\cdot)$ $\chi_{405}(301,\cdot)$ $\chi_{405}(331,\cdot)$ $\chi_{405}(346,\cdot)$ $\chi_{405}(376,\cdot)$ $\chi_{405}(391,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{27})$
Fixed field:	Number field defined by a degree 27 polynomial

Values on generators

$(326,82)$ → $(e\left(\frac{10}{27}\right),1)$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 405 }(31, a)$	$1$	$1$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{20}{27}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{22}{27}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{8}{27}\right)$	$e\left(\frac{13}{27}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{9}\right)$

Gauss sum

Jacobi sum

Kloosterman sum