Dirichlet character χ323(311,⋅)\chi_{323}(311,\cdot)

• Label: 323.311
• Modulus: $323$
• Conductor: $323$
• Order: $48$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$323$
Conductor:	$323$
Order:	$48$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 323.z

$\chi_{323}(7,\cdot)$ $\chi_{323}(11,\cdot)$ $\chi_{323}(45,\cdot)$ $\chi_{323}(125,\cdot)$ $\chi_{323}(159,\cdot)$ $\chi_{323}(163,\cdot)$ $\chi_{323}(182,\cdot)$ $\chi_{323}(197,\cdot)$ $\chi_{323}(201,\cdot)$ $\chi_{323}(216,\cdot)$ $\chi_{323}(235,\cdot)$ $\chi_{323}(258,\cdot)$ $\chi_{323}(277,\cdot)$ $\chi_{323}(292,\cdot)$ $\chi_{323}(296,\cdot)$ $\chi_{323}(311,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{48})$
Fixed field:	Number field defined by a degree 48 polynomial

Values on generators

$(20,154)$ → $(e\left(\frac{5}{16}\right),e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 323 }(311, a)$	$-1$	$1$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{3}{16}\right)$

Gauss sum

Jacobi sum

Kloosterman sum