Dirichlet character χ2381(500,⋅)\chi_{2381}(500,\cdot)

• Label: 2381.500
• Modulus: $2381$
• Conductor: $2381$
• Order: $119$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2381$
Conductor:	$2381$
Order:	$119$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2381.p

$\chi_{2381}(16,\cdot)$ $\chi_{2381}(17,\cdot)$ $\chi_{2381}(20,\cdot)$ $\chi_{2381}(25,\cdot)$ $\chi_{2381}(28,\cdot)$ $\chi_{2381}(35,\cdot)$ $\chi_{2381}(49,\cdot)$ $\chi_{2381}(82,\cdot)$ $\chi_{2381}(141,\cdot)$ $\chi_{2381}(151,\cdot)$ $\chi_{2381}(173,\cdot)$ $\chi_{2381}(186,\cdot)$ $\chi_{2381}(256,\cdot)$ $\chi_{2381}(272,\cdot)$ $\chi_{2381}(289,\cdot)$ $\chi_{2381}(320,\cdot)$ $\chi_{2381}(340,\cdot)$ $\chi_{2381}(358,\cdot)$ $\chi_{2381}(381,\cdot)$ $\chi_{2381}(387,\cdot)$ $\chi_{2381}(400,\cdot)$ $\chi_{2381}(425,\cdot)$ $\chi_{2381}(439,\cdot)$ $\chi_{2381}(446,\cdot)$ $\chi_{2381}(473,\cdot)$ $\chi_{2381}(476,\cdot)$ $\chi_{2381}(500,\cdot)$ $\chi_{2381}(523,\cdot)$ $\chi_{2381}(552,\cdot)$ $\chi_{2381}(589,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{119})$
Fixed field:	Number field defined by a degree 119 polynomial (not computed)

Values on generators

$3$ → $e\left(\frac{89}{119}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 2381 }(500, a)$	$1$	$1$	$e\left(\frac{101}{119}\right)$	$e\left(\frac{89}{119}\right)$	$e\left(\frac{83}{119}\right)$	$e\left(\frac{62}{119}\right)$	$e\left(\frac{71}{119}\right)$	$e\left(\frac{66}{119}\right)$	$e\left(\frac{65}{119}\right)$	$e\left(\frac{59}{119}\right)$	$e\left(\frac{44}{119}\right)$	$e\left(\frac{87}{119}\right)$