Dirichlet character χ100014(503,⋅)\chi_{100014}(503,\cdot)

• Label: 100014.503
• Modulus: $100014$
• Conductor: $50007$
• Order: $2730$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$100014$
Conductor:	$50007$
Order:	$2730$
Real:	no
Primitive:	no, induced from $\chi_{50007}(503,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 100014.lt

$\chi_{100014}(47,\cdot)$ $\chi_{100014}(53,\cdot)$ $\chi_{100014}(503,\cdot)$ $\chi_{100014}(695,\cdot)$ $\chi_{100014}(983,\cdot)$ $\chi_{100014}(1007,\cdot)$ $\chi_{100014}(1061,\cdot)$ $\chi_{100014}(1181,\cdot)$ $\chi_{100014}(1259,\cdot)$ $\chi_{100014}(1475,\cdot)$ $\chi_{100014}(1481,\cdot)$ $\chi_{100014}(1529,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{1365})$
Fixed field:	Number field defined by a degree 2730 polynomial (not computed)

Values on generators

$(66677,1267,32707)$ → $(-1,e\left(\frac{11}{78}\right),e\left(\frac{86}{105}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{ 100014 }(503, a)$	$1$	$1$	$e\left(\frac{977}{2730}\right)$	$e\left(\frac{293}{910}\right)$	$e\left(\frac{2117}{2730}\right)$	$e\left(\frac{1007}{1365}\right)$	$e\left(\frac{617}{1365}\right)$	$e\left(\frac{42}{65}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{977}{1365}\right)$	$e\left(\frac{902}{1365}\right)$	$e\left(\frac{8}{91}\right)$