Dirichlet character χ85600(1419,⋅)\chi_{85600}(1419,\cdot)

• Label: 85600.1419
• 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

$(26751,32101,82177,16801)$ → $(-1,e\left(\frac{5}{8}\right),e\left(\frac{9}{10}\right),e\left(\frac{45}{106}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 85600 }(1419, a)$	$1$	$1$	$e\left(\frac{831}{2120}\right)$	$e\left(\frac{107}{212}\right)$	$e\left(\frac{831}{1060}\right)$	$e\left(\frac{773}{2120}\right)$	$e\left(\frac{887}{2120}\right)$	$e\left(\frac{271}{530}\right)$	$e\left(\frac{399}{2120}\right)$	$e\left(\frac{1901}{2120}\right)$	$e\left(\frac{499}{1060}\right)$	$e\left(\frac{373}{2120}\right)$