Dirichlet character χ39(2,⋅)\chi_{39}(2,\cdot)

• Label: 39.2
• Modulus: $39$
• Conductor: $39$
• Order: $12$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$39$
Conductor:	$39$
Order:	$12$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 39.k

$\chi_{39}(2,\cdot)$ $\chi_{39}(11,\cdot)$ $\chi_{39}(20,\cdot)$ $\chi_{39}(32,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	$\Q(\zeta_{39})^+$

Values on generators

$(14,28)$ → $(-1,e\left(\frac{1}{12}\right))$

Values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$14$	$16$	$17$
$\chi_{ 39 }(2, a)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$i$	$e\left(\frac{11}{12}\right)$	$-i$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Gauss sum

Jacobi sum

Kloosterman sum