Dirichlet character χ110(31,⋅)\chi_{110}(31,\cdot)

• Label: 110.31
• Modulus: $110$
• Conductor: $11$
• Order: $5$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$110$
Conductor:	$11$
Order:	$5$
Real:	no
Primitive:	no, induced from $\chi_{11}(9,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 110.g

$\chi_{110}(31,\cdot)$ $\chi_{110}(71,\cdot)$ $\chi_{110}(81,\cdot)$ $\chi_{110}(91,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{5})$
Fixed field:	$\Q(\zeta_{11})^+$

Values on generators

$(67,101)$ → $(1,e\left(\frac{3}{5}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$13$	$17$	$19$	$21$	$23$	$27$	$29$
$\chi_{ 110 }(31, a)$	$1$	$1$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{4}{5}\right)$	$1$	$1$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{5}\right)$

Gauss sum

Jacobi sum

Kloosterman sum