Dirichlet character χ7800(4999,⋅)\chi_{7800}(4999,\cdot)

• Label: 7800.4999
• Modulus: $7800$
• Conductor: $260$
• Order: $12$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$7800$
Conductor:	$260$
Order:	$12$
Real:	no
Primitive:	no, induced from $\chi_{260}(59,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 7800.gi

$\chi_{7800}(799,\cdot)$ $\chi_{7800}(4999,\cdot)$ $\chi_{7800}(6199,\cdot)$ $\chi_{7800}(7399,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{12})$
Fixed field:	12.12.114698265218368000000.1

Values on generators

$(1951,3901,5201,7177,4201)$ → $(-1,1,1,-1,e\left(\frac{11}{12}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 7800 }(4999, a)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-i$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{6}\right)$