Dirichlet character χ85600(381,⋅)\chi_{85600}(381,\cdot)

• Label: 85600.381
• Modulus: $85600$
• Conductor: $85600$
• Order: $2120$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

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

Galois orbit 85600.ij

$\chi_{85600}(21,\cdot)$ $\chi_{85600}(181,\cdot)$ $\chi_{85600}(221,\cdot)$ $\chi_{85600}(341,\cdot)$ $\chi_{85600}(381,\cdot)$ $\chi_{85600}(541,\cdot)$ $\chi_{85600}(581,\cdot)$ $\chi_{85600}(781,\cdot)$ $\chi_{85600}(821,\cdot)$ $\chi_{85600}(861,\cdot)$ $\chi_{85600}(981,\cdot)$ $\chi_{85600}(1021,\cdot)$ $\chi_{85600}(1061,\cdot)$ $\chi_{85600}(1141,\cdot)$ $\chi_{85600}(1261,\cdot)$ $\chi_{85600}(1381,\cdot)$ $\chi_{85600}(1461,\cdot)$ $\chi_{85600}(1541,\cdot)$

Related number fields

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

Values on generators

$(26751,32101,82177,16801)$ → $(1,e\left(\frac{3}{8}\right),e\left(\frac{2}{5}\right),e\left(\frac{13}{106}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 85600 }(381, a)$	$-1$	$1$	$e\left(\frac{1081}{2120}\right)$	$e\left(\frac{5}{212}\right)$	$e\left(\frac{21}{1060}\right)$	$e\left(\frac{2063}{2120}\right)$	$e\left(\frac{1997}{2120}\right)$	$e\left(\frac{68}{265}\right)$	$e\left(\frac{829}{2120}\right)$	$e\left(\frac{1131}{2120}\right)$	$e\left(\frac{269}{1060}\right)$	$e\left(\frac{1123}{2120}\right)$