Dirichlet character χ103(100,⋅)\chi_{103}(100,\cdot)

• Label: 103.100
• Modulus: $103$
• Conductor: $103$
• Order: $17$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$103$
Conductor:	$103$
Order:	$17$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 103.e

$\chi_{103}(8,\cdot)$ $\chi_{103}(9,\cdot)$ $\chi_{103}(13,\cdot)$ $\chi_{103}(14,\cdot)$ $\chi_{103}(23,\cdot)$ $\chi_{103}(30,\cdot)$ $\chi_{103}(34,\cdot)$ $\chi_{103}(61,\cdot)$ $\chi_{103}(64,\cdot)$ $\chi_{103}(66,\cdot)$ $\chi_{103}(72,\cdot)$ $\chi_{103}(76,\cdot)$ $\chi_{103}(79,\cdot)$ $\chi_{103}(81,\cdot)$ $\chi_{103}(93,\cdot)$ $\chi_{103}(100,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{17})$
Fixed field:	Number field defined by a degree 17 polynomial

Values on generators

$5$ → $e\left(\frac{15}{17}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 103 }(100, a)$	$1$	$1$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{7}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{15}{17}\right)$	$e\left(\frac{4}{17}\right)$	$e\left(\frac{9}{17}\right)$	$e\left(\frac{8}{17}\right)$	$e\left(\frac{14}{17}\right)$	$e\left(\frac{12}{17}\right)$	$e\left(\frac{14}{17}\right)$

Gauss sum

Jacobi sum

Kloosterman sum