Dirichlet character χ700(501,⋅)\chi_{700}(501,\cdot)

• Label: 700.501
• Modulus: $700$
• Conductor: $7$
• Order: $3$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$700$
Conductor:	$7$
Order:	$3$
Real:	no
Primitive:	no, induced from $\chi_{7}(4,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 700.i

$\chi_{700}(401,\cdot)$ $\chi_{700}(501,\cdot)$

Related number fields

Field of values:	$\mathbb{Q}(\zeta_3)$
Fixed field:	$\Q(\zeta_{7})^+$

Values on generators

$(351,477,101)$ → $(1,1,e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{ 700 }(501, a)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum