Dirichlet character χ176(17,⋅)\chi_{176}(17,\cdot)

• Label: 176.17
• Modulus: $176$
• Conductor: $11$
• Order: $10$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$176$
Conductor:	$11$
Order:	$10$
Real:	no
Primitive:	no, induced from $\chi_{11}(6,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 176.n

$\chi_{176}(17,\cdot)$ $\chi_{176}(129,\cdot)$ $\chi_{176}(145,\cdot)$ $\chi_{176}(161,\cdot)$

Related number fields

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

Values on generators

$(111,133,145)$ → $(1,1,e\left(\frac{9}{10}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 176 }(17, a)$	$-1$	$1$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$

Gauss sum

Jacobi sum

Kloosterman sum