Dirichlet character χ176(149,⋅)\chi_{176}(149,\cdot)

• Label: 176.149
• Modulus: $176$
• Conductor: $176$
• Order: $20$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$176$
Conductor:	$176$
Order:	$20$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 176.u

$\chi_{176}(13,\cdot)$ $\chi_{176}(29,\cdot)$ $\chi_{176}(61,\cdot)$ $\chi_{176}(85,\cdot)$ $\chi_{176}(101,\cdot)$ $\chi_{176}(117,\cdot)$ $\chi_{176}(149,\cdot)$ $\chi_{176}(173,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	20.0.200317132330035063121671003054276608.1

Values on generators

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

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$13$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 176 }(149, a)$	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{9}{20}\right)$	$-i$	$-1$

Gauss sum

Jacobi sum

Kloosterman sum