Dirichlet character χ197(158,⋅)\chi_{197}(158,\cdot)

• Label: 197.158
• Modulus: $197$
• Conductor: $197$
• Order: $49$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$197$
Conductor:	$197$
Order:	$49$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 197.g

$\chi_{197}(16,\cdot)$ $\chi_{197}(23,\cdot)$ $\chi_{197}(24,\cdot)$ $\chi_{197}(28,\cdot)$ $\chi_{197}(29,\cdot)$ $\chi_{197}(34,\cdot)$ $\chi_{197}(37,\cdot)$ $\chi_{197}(40,\cdot)$ $\chi_{197}(42,\cdot)$ $\chi_{197}(49,\cdot)$ $\chi_{197}(51,\cdot)$ $\chi_{197}(53,\cdot)$ $\chi_{197}(54,\cdot)$ $\chi_{197}(59,\cdot)$ $\chi_{197}(60,\cdot)$ $\chi_{197}(61,\cdot)$ $\chi_{197}(63,\cdot)$ $\chi_{197}(70,\cdot)$ $\chi_{197}(76,\cdot)$ $\chi_{197}(81,\cdot)$ $\chi_{197}(85,\cdot)$ $\chi_{197}(88,\cdot)$ $\chi_{197}(90,\cdot)$ $\chi_{197}(100,\cdot)$ $\chi_{197}(101,\cdot)$ $\chi_{197}(105,\cdot)$ $\chi_{197}(132,\cdot)$ $\chi_{197}(133,\cdot)$ $\chi_{197}(135,\cdot)$ $\chi_{197}(142,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{49})$
Fixed field:	Number field defined by a degree 49 polynomial

Values on generators

$2$ → $e\left(\frac{27}{49}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 197 }(158, a)$	$1$	$1$	$e\left(\frac{27}{49}\right)$	$e\left(\frac{36}{49}\right)$	$e\left(\frac{5}{49}\right)$	$e\left(\frac{2}{49}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{22}{49}\right)$	$e\left(\frac{32}{49}\right)$	$e\left(\frac{23}{49}\right)$	$e\left(\frac{29}{49}\right)$	$e\left(\frac{48}{49}\right)$

Gauss sum

Jacobi sum

Kloosterman sum