Dirichlet character χ85600(379,⋅)\chi_{85600}(379,\cdot)

• Label: 85600.379
• Modulus: $85600$
• Conductor: $85600$
• Order: $2120$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$85600$
Conductor:	$85600$
Order:	$2120$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 85600.ig

$\chi_{85600}(59,\cdot)$ $\chi_{85600}(139,\cdot)$ $\chi_{85600}(179,\cdot)$ $\chi_{85600}(219,\cdot)$ $\chi_{85600}(259,\cdot)$ $\chi_{85600}(339,\cdot)$ $\chi_{85600}(379,\cdot)$ $\chi_{85600}(419,\cdot)$ $\chi_{85600}(459,\cdot)$ $\chi_{85600}(619,\cdot)$ $\chi_{85600}(659,\cdot)$ $\chi_{85600}(739,\cdot)$ $\chi_{85600}(819,\cdot)$ $\chi_{85600}(1059,\cdot)$ $\chi_{85600}(1179,\cdot)$ $\chi_{85600}(1259,\cdot)$ $\chi_{85600}(1339,\cdot)$ $\chi_{85600}(1379,\cdot)$ $\chi_{85600}(1419,\cdot)$ $\chi_{85600}(1459,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{2120})$
Fixed field:	Number field defined by a degree 2120 polynomial (not computed)

Values on generators

$(26751,32101,82177,16801)$ → $(-1,e\left(\frac{1}{8}\right),e\left(\frac{1}{10}\right),e\left(\frac{33}{106}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 85600 }(379, a)$	$1$	$1$	$e\left(\frac{779}{2120}\right)$	$e\left(\frac{135}{212}\right)$	$e\left(\frac{779}{1060}\right)$	$e\left(\frac{1217}{2120}\right)$	$e\left(\frac{283}{2120}\right)$	$e\left(\frac{439}{530}\right)$	$e\left(\frac{971}{2120}\right)$	$e\left(\frac{9}{2120}\right)$	$e\left(\frac{691}{1060}\right)$	$e\left(\frac{217}{2120}\right)$