Dirichlet character χ812(471,⋅)\chi_{812}(471,\cdot)

• Label: 812.471
• Modulus: $812$
• Conductor: $812$
• Order: $42$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$812$
Conductor:	$812$
Order:	$42$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 812.bn

$\chi_{812}(23,\cdot)$ $\chi_{812}(107,\cdot)$ $\chi_{812}(123,\cdot)$ $\chi_{812}(219,\cdot)$ $\chi_{812}(431,\cdot)$ $\chi_{812}(459,\cdot)$ $\chi_{812}(471,\cdot)$ $\chi_{812}(487,\cdot)$ $\chi_{812}(571,\cdot)$ $\chi_{812}(683,\cdot)$ $\chi_{812}(779,\cdot)$ $\chi_{812}(807,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 42 polynomial

Values on generators

$(407,465,785)$ → $(-1,e\left(\frac{1}{3}\right),e\left(\frac{3}{7}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 812 }(471, a)$	$-1$	$1$	$e\left(\frac{41}{42}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{23}{42}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{14}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{42}\right)$	$e\left(\frac{31}{42}\right)$	$e\left(\frac{4}{21}\right)$

Gauss sum

Jacobi sum

Kloosterman sum