Dirichlet character χ163(52,⋅)\chi_{163}(52,\cdot)

• Label: 163.52
• Modulus: $163$
• Conductor: $163$
• Order: $162$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$163$
Conductor:	$163$
Order:	$162$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 163.j

$\chi_{163}(2,\cdot)$ $\chi_{163}(3,\cdot)$ $\chi_{163}(7,\cdot)$ $\chi_{163}(11,\cdot)$ $\chi_{163}(12,\cdot)$ $\chi_{163}(18,\cdot)$ $\chi_{163}(19,\cdot)$ $\chi_{163}(20,\cdot)$ $\chi_{163}(29,\cdot)$ $\chi_{163}(32,\cdot)$ $\chi_{163}(42,\cdot)$ $\chi_{163}(44,\cdot)$ $\chi_{163}(45,\cdot)$ $\chi_{163}(50,\cdot)$ $\chi_{163}(52,\cdot)$ $\chi_{163}(63,\cdot)$ $\chi_{163}(66,\cdot)$ $\chi_{163}(67,\cdot)$ $\chi_{163}(68,\cdot)$ $\chi_{163}(70,\cdot)$ $\chi_{163}(72,\cdot)$ $\chi_{163}(73,\cdot)$ $\chi_{163}(75,\cdot)$ $\chi_{163}(76,\cdot)$ $\chi_{163}(79,\cdot)$ $\chi_{163}(80,\cdot)$ $\chi_{163}(82,\cdot)$ $\chi_{163}(89,\cdot)$ $\chi_{163}(92,\cdot)$ $\chi_{163}(94,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{81})$
Fixed field:	Number field defined by a degree 162 polynomial (not computed)

Values on generators

$2$ → $e\left(\frac{53}{162}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 163 }(52, a)$	$-1$	$1$	$e\left(\frac{53}{162}\right)$	$e\left(\frac{7}{162}\right)$	$e\left(\frac{53}{81}\right)$	$e\left(\frac{49}{54}\right)$	$e\left(\frac{10}{27}\right)$	$e\left(\frac{143}{162}\right)$	$e\left(\frac{53}{54}\right)$	$e\left(\frac{7}{81}\right)$	$e\left(\frac{19}{81}\right)$	$e\left(\frac{61}{162}\right)$

Gauss sum

Jacobi sum

Kloosterman sum