Dirichlet character χ247(193,⋅)\chi_{247}(193,\cdot)

• Label: 247.193
• Modulus: $247$
• Conductor: $247$
• Order: $36$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$247$
Conductor:	$247$
Order:	$36$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 247.br

$\chi_{247}(2,\cdot)$ $\chi_{247}(32,\cdot)$ $\chi_{247}(41,\cdot)$ $\chi_{247}(72,\cdot)$ $\chi_{247}(110,\cdot)$ $\chi_{247}(124,\cdot)$ $\chi_{247}(128,\cdot)$ $\chi_{247}(154,\cdot)$ $\chi_{247}(162,\cdot)$ $\chi_{247}(193,\cdot)$ $\chi_{247}(223,\cdot)$ $\chi_{247}(241,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	36.36.172883305869849387893002611628480390541620325819249742650713178237814353492521813.2

Values on generators

$(210,40)$ → $(e\left(\frac{7}{12}\right),e\left(\frac{13}{18}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 247 }(193, a)$	$1$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{36}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{9}\right)$	$-i$

Gauss sum

Jacobi sum

Kloosterman sum