Dirichlet character χ197(120,⋅)\chi_{197}(120,\cdot)

• Label: 197.120
• Modulus: $197$
• Conductor: $197$
• Order: $28$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$197$
Conductor:	$197$
Order:	$28$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 197.f

$\chi_{197}(20,\cdot)$ $\chi_{197}(68,\cdot)$ $\chi_{197}(69,\cdot)$ $\chi_{197}(77,\cdot)$ $\chi_{197}(84,\cdot)$ $\chi_{197}(87,\cdot)$ $\chi_{197}(110,\cdot)$ $\chi_{197}(113,\cdot)$ $\chi_{197}(120,\cdot)$ $\chi_{197}(128,\cdot)$ $\chi_{197}(129,\cdot)$ $\chi_{197}(177,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{28})$
Fixed field:	Number field defined by a degree 28 polynomial

Values on generators

$2$ → $e\left(\frac{11}{28}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 197 }(120, a)$	$-1$	$1$	$e\left(\frac{11}{28}\right)$	$e\left(\frac{3}{28}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{27}{28}\right)$	$-1$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{5}{28}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{11}{28}\right)$

Gauss sum

Jacobi sum

Kloosterman sum