Dirichlet character χ377(53,⋅)\chi_{377}(53,\cdot)

• Label: 377.53
• Modulus: $377$
• Conductor: $29$
• Order: $7$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$377$
Conductor:	$29$
Order:	$7$
Real:	no
Primitive:	no, induced from $\chi_{29}(24,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 377.o

$\chi_{377}(53,\cdot)$ $\chi_{377}(170,\cdot)$ $\chi_{377}(248,\cdot)$ $\chi_{377}(313,\cdot)$ $\chi_{377}(326,\cdot)$ $\chi_{377}(339,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{7})$
Fixed field:	7.7.594823321.1

Values on generators

$(262,118)$ → $(1,e\left(\frac{2}{7}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 377 }(53, a)$	$1$	$1$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$

Gauss sum

Jacobi sum

Kloosterman sum