Dirichlet character χ261(103,⋅)\chi_{261}(103,\cdot)

• Label: 261.103
• Modulus: $261$
• Conductor: $261$
• Order: $21$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$261$
Conductor:	$261$
Order:	$21$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 261.q

$\chi_{261}(7,\cdot)$ $\chi_{261}(16,\cdot)$ $\chi_{261}(25,\cdot)$ $\chi_{261}(49,\cdot)$ $\chi_{261}(52,\cdot)$ $\chi_{261}(94,\cdot)$ $\chi_{261}(103,\cdot)$ $\chi_{261}(112,\cdot)$ $\chi_{261}(139,\cdot)$ $\chi_{261}(169,\cdot)$ $\chi_{261}(223,\cdot)$ $\chi_{261}(256,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 21 polynomial

Values on generators

$(146,118)$ → $(e\left(\frac{1}{3}\right),e\left(\frac{1}{7}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$5$	$7$	$8$	$10$	$11$	$13$	$14$	$16$
$\chi_{ 261 }(103, a)$	$1$	$1$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{20}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{19}{21}\right)$

Gauss sum

Jacobi sum

Kloosterman sum