Dirichlet character χ740(199,⋅)\chi_{740}(199,\cdot)

• Label: 740.199
• Modulus: $740$
• Conductor: $740$
• Order: $12$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$740$
Conductor:	$740$
Order:	$12$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 740.bo

$\chi_{740}(119,\cdot)$ $\chi_{740}(199,\cdot)$ $\chi_{740}(319,\cdot)$ $\chi_{740}(399,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.12.11386727793885466432000000.1

Values on generators

$(371,297,261)$ → $(-1,-1,e\left(\frac{11}{12}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 740 }(199, a)$	$1$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$	$-i$	$-1$

Gauss sum

Jacobi sum

Kloosterman sum