Dirichlet character χ71(45,⋅)\chi_{71}(45,\cdot)

• Label: 71.45
• Modulus: $71$
• Conductor: $71$
• Order: $7$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$71$
Conductor:	$71$
Order:	$7$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 71.d

$\chi_{71}(20,\cdot)$ $\chi_{71}(30,\cdot)$ $\chi_{71}(32,\cdot)$ $\chi_{71}(37,\cdot)$ $\chi_{71}(45,\cdot)$ $\chi_{71}(48,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{7})$
Fixed field:	7.7.128100283921.1

Values on generators

$7$ → $e\left(\frac{1}{7}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 71 }(45, a)$	$1$	$1$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{5}{7}\right)$	$1$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{3}{7}\right)$

Gauss sum

Jacobi sum

Kloosterman sum