Dirichlet character χ376(337,⋅)\chi_{376}(337,\cdot)

• Label: 376.337
• Modulus: $376$
• Conductor: $47$
• Order: $23$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$376$
Conductor:	$47$
Order:	$23$
Real:	no
Primitive:	no, induced from $\chi_{47}(8,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 376.i

$\chi_{376}(9,\cdot)$ $\chi_{376}(17,\cdot)$ $\chi_{376}(25,\cdot)$ $\chi_{376}(49,\cdot)$ $\chi_{376}(65,\cdot)$ $\chi_{376}(81,\cdot)$ $\chi_{376}(89,\cdot)$ $\chi_{376}(97,\cdot)$ $\chi_{376}(121,\cdot)$ $\chi_{376}(145,\cdot)$ $\chi_{376}(153,\cdot)$ $\chi_{376}(169,\cdot)$ $\chi_{376}(177,\cdot)$ $\chi_{376}(209,\cdot)$ $\chi_{376}(225,\cdot)$ $\chi_{376}(241,\cdot)$ $\chi_{376}(249,\cdot)$ $\chi_{376}(289,\cdot)$ $\chi_{376}(337,\cdot)$ $\chi_{376}(345,\cdot)$ $\chi_{376}(353,\cdot)$ $\chi_{376}(361,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{23})$
Fixed field:	Number field defined by a degree 23 polynomial

Values on generators

$(95,189,193)$ → $(1,1,e\left(\frac{4}{23}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 376 }(337, a)$	$1$	$1$	$e\left(\frac{11}{23}\right)$	$e\left(\frac{4}{23}\right)$	$e\left(\frac{13}{23}\right)$	$e\left(\frac{22}{23}\right)$	$e\left(\frac{5}{23}\right)$	$e\left(\frac{21}{23}\right)$	$e\left(\frac{15}{23}\right)$	$e\left(\frac{18}{23}\right)$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{1}{23}\right)$

Gauss sum

Jacobi sum

Kloosterman sum