Dirichlet character χ812(499,⋅)\chi_{812}(499,\cdot)

• Label: 812.499
• 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.br

$\chi_{812}(51,\cdot)$ $\chi_{812}(67,\cdot)$ $\chi_{812}(151,\cdot)$ $\chi_{812}(179,\cdot)$ $\chi_{812}(207,\cdot)$ $\chi_{812}(303,\cdot)$ $\chi_{812}(415,\cdot)$ $\chi_{812}(499,\cdot)$ $\chi_{812}(515,\cdot)$ $\chi_{812}(527,\cdot)$ $\chi_{812}(555,\cdot)$ $\chi_{812}(767,\cdot)$

Related number fields

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

Values on generators

$(407,465,785)$ → $(-1,e\left(\frac{1}{3}\right),e\left(\frac{3}{14}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$19$	$23$	$25$
$\chi_{ 812 }(499, a)$	$-1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{19}{42}\right)$	$e\left(\frac{16}{21}\right)$

Gauss sum

Jacobi sum

Kloosterman sum