Dirichlet character χ85600(1437,⋅)\chi_{85600}(1437,\cdot)

• Label: 85600.1437
• 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.io

$\chi_{85600}(77,\cdot)$ $\chi_{85600}(133,\cdot)$ $\chi_{85600}(317,\cdot)$ $\chi_{85600}(613,\cdot)$ $\chi_{85600}(773,\cdot)$ $\chi_{85600}(853,\cdot)$ $\chi_{85600}(877,\cdot)$ $\chi_{85600}(933,\cdot)$ $\chi_{85600}(1013,\cdot)$ $\chi_{85600}(1037,\cdot)$ $\chi_{85600}(1173,\cdot)$ $\chi_{85600}(1197,\cdot)$ $\chi_{85600}(1413,\cdot)$ $\chi_{85600}(1437,\cdot)$

Related number fields

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

Values on generators

$(26751,32101,82177,16801)$ → $(1,e\left(\frac{3}{8}\right),e\left(\frac{9}{20}\right),e\left(\frac{63}{106}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 85600 }(1437, a)$	$1$	$1$	$e\left(\frac{1863}{2120}\right)$	$e\left(\frac{59}{106}\right)$	$e\left(\frac{803}{1060}\right)$	$e\left(\frac{319}{2120}\right)$	$e\left(\frac{1051}{2120}\right)$	$e\left(\frac{621}{1060}\right)$	$e\left(\frac{177}{2120}\right)$	$e\left(\frac{923}{2120}\right)$	$e\left(\frac{13}{265}\right)$	$e\left(\frac{1349}{2120}\right)$