Dirichlet character χ103(11,⋅)\chi_{103}(11,\cdot)

• Label: 103.11
• Modulus: $103$
• Conductor: $103$
• Order: $102$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$103$
Conductor:	$103$
Order:	$102$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 103.h

$\chi_{103}(5,\cdot)$ $\chi_{103}(6,\cdot)$ $\chi_{103}(11,\cdot)$ $\chi_{103}(12,\cdot)$ $\chi_{103}(20,\cdot)$ $\chi_{103}(21,\cdot)$ $\chi_{103}(35,\cdot)$ $\chi_{103}(40,\cdot)$ $\chi_{103}(43,\cdot)$ $\chi_{103}(44,\cdot)$ $\chi_{103}(45,\cdot)$ $\chi_{103}(48,\cdot)$ $\chi_{103}(51,\cdot)$ $\chi_{103}(53,\cdot)$ $\chi_{103}(54,\cdot)$ $\chi_{103}(62,\cdot)$ $\chi_{103}(65,\cdot)$ $\chi_{103}(67,\cdot)$ $\chi_{103}(70,\cdot)$ $\chi_{103}(71,\cdot)$ $\chi_{103}(74,\cdot)$ $\chi_{103}(75,\cdot)$ $\chi_{103}(77,\cdot)$ $\chi_{103}(78,\cdot)$ $\chi_{103}(84,\cdot)$ $\chi_{103}(85,\cdot)$ $\chi_{103}(86,\cdot)$ $\chi_{103}(87,\cdot)$ $\chi_{103}(88,\cdot)$ $\chi_{103}(96,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{51})$
Fixed field:	Number field defined by a degree 102 polynomial (not computed)

Values on generators

$5$ → $e\left(\frac{61}{102}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 103 }(11, a)$	$-1$	$1$	$e\left(\frac{16}{51}\right)$	$e\left(\frac{11}{34}\right)$	$e\left(\frac{32}{51}\right)$	$e\left(\frac{61}{102}\right)$	$e\left(\frac{65}{102}\right)$	$e\left(\frac{20}{51}\right)$	$e\left(\frac{16}{17}\right)$	$e\left(\frac{11}{17}\right)$	$e\left(\frac{31}{34}\right)$	$e\left(\frac{49}{102}\right)$

Gauss sum

Jacobi sum

Kloosterman sum