Dirichlet character χ197(46,⋅)\chi_{197}(46,\cdot)

• Label: 197.46
• Modulus: $197$
• Conductor: $197$
• Order: $196$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$197$
Conductor:	$197$
Order:	$196$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 197.i

$\chi_{197}(2,\cdot)$ $\chi_{197}(3,\cdot)$ $\chi_{197}(5,\cdot)$ $\chi_{197}(8,\cdot)$ $\chi_{197}(11,\cdot)$ $\chi_{197}(12,\cdot)$ $\chi_{197}(13,\cdot)$ $\chi_{197}(17,\cdot)$ $\chi_{197}(18,\cdot)$ $\chi_{197}(21,\cdot)$ $\chi_{197}(27,\cdot)$ $\chi_{197}(30,\cdot)$ $\chi_{197}(31,\cdot)$ $\chi_{197}(32,\cdot)$ $\chi_{197}(35,\cdot)$ $\chi_{197}(38,\cdot)$ $\chi_{197}(44,\cdot)$ $\chi_{197}(45,\cdot)$ $\chi_{197}(46,\cdot)$ $\chi_{197}(48,\cdot)$ $\chi_{197}(50,\cdot)$ $\chi_{197}(52,\cdot)$ $\chi_{197}(56,\cdot)$ $\chi_{197}(57,\cdot)$ $\chi_{197}(58,\cdot)$ $\chi_{197}(66,\cdot)$ $\chi_{197}(67,\cdot)$ $\chi_{197}(71,\cdot)$ $\chi_{197}(72,\cdot)$ $\chi_{197}(73,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{196})$
Fixed field:	Number field defined by a degree 196 polynomial (not computed)

Values on generators

$2$ → $e\left(\frac{121}{196}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 197 }(46, a)$	$-1$	$1$	$e\left(\frac{121}{196}\right)$	$e\left(\frac{145}{196}\right)$	$e\left(\frac{23}{98}\right)$	$e\left(\frac{185}{196}\right)$	$e\left(\frac{5}{14}\right)$	$e\left(\frac{13}{98}\right)$	$e\left(\frac{167}{196}\right)$	$e\left(\frac{47}{98}\right)$	$e\left(\frac{55}{98}\right)$	$e\left(\frac{177}{196}\right)$

Gauss sum

Jacobi sum

Kloosterman sum