Dirichlet character χ812(271,⋅)\chi_{812}(271,\cdot)

• Label: 812.271
• Modulus: $812$
• Conductor: $812$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$812$
Conductor:	$812$
Order:	$84$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 812.bu

$\chi_{812}(3,\cdot)$ $\chi_{812}(19,\cdot)$ $\chi_{812}(31,\cdot)$ $\chi_{812}(47,\cdot)$ $\chi_{812}(131,\cdot)$ $\chi_{812}(143,\cdot)$ $\chi_{812}(159,\cdot)$ $\chi_{812}(171,\cdot)$ $\chi_{812}(243,\cdot)$ $\chi_{812}(271,\cdot)$ $\chi_{812}(311,\cdot)$ $\chi_{812}(327,\cdot)$ $\chi_{812}(367,\cdot)$ $\chi_{812}(395,\cdot)$ $\chi_{812}(467,\cdot)$ $\chi_{812}(479,\cdot)$ $\chi_{812}(495,\cdot)$ $\chi_{812}(507,\cdot)$ $\chi_{812}(591,\cdot)$ $\chi_{812}(607,\cdot)$ $\chi_{812}(619,\cdot)$ $\chi_{812}(635,\cdot)$ $\chi_{812}(675,\cdot)$ $\chi_{812}(775,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

$(407,465,785)$ → $(-1,e\left(\frac{5}{6}\right),e\left(\frac{23}{28}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 812 }(271, a)$	$-1$	$1$	$e\left(\frac{37}{84}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{37}{42}\right)$	$e\left(\frac{31}{84}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{28}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{84}\right)$	$e\left(\frac{25}{42}\right)$	$e\left(\frac{10}{21}\right)$

Gauss sum

Jacobi sum

Kloosterman sum