Dirichlet character χ405(41,⋅)\chi_{405}(41,\cdot)

• Label: 405.41
• Modulus: $405$
• Conductor: $81$
• Order: $54$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$405$
Conductor:	$81$
Order:	$54$
Real:	no
Primitive:	no, induced from $\chi_{81}(41,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 405.u

$\chi_{405}(11,\cdot)$ $\chi_{405}(41,\cdot)$ $\chi_{405}(56,\cdot)$ $\chi_{405}(86,\cdot)$ $\chi_{405}(101,\cdot)$ $\chi_{405}(131,\cdot)$ $\chi_{405}(146,\cdot)$ $\chi_{405}(176,\cdot)$ $\chi_{405}(191,\cdot)$ $\chi_{405}(221,\cdot)$ $\chi_{405}(236,\cdot)$ $\chi_{405}(266,\cdot)$ $\chi_{405}(281,\cdot)$ $\chi_{405}(311,\cdot)$ $\chi_{405}(326,\cdot)$ $\chi_{405}(356,\cdot)$ $\chi_{405}(371,\cdot)$ $\chi_{405}(401,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{27})$
Fixed field:	Number field defined by a degree 54 polynomial

Values on generators

$(326,82)$ → $(e\left(\frac{53}{54}\right),1)$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$19$
$\chi_{ 405 }(41, a)$	$-1$	$1$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{26}{27}\right)$	$e\left(\frac{19}{27}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{41}{54}\right)$	$e\left(\frac{23}{27}\right)$	$e\left(\frac{37}{54}\right)$	$e\left(\frac{25}{27}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{9}\right)$

Gauss sum

Jacobi sum

Kloosterman sum