Dirichlet character χ7488(6587,⋅)\chi_{7488}(6587,\cdot)

• Label: 7488.6587
• Modulus: $7488$
• Conductor: $2496$
• Order: $48$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$7488$
Conductor:	$2496$
Order:	$48$
Real:	no
Primitive:	no, induced from $\chi_{2496}(1595,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 7488.nv

$\chi_{7488}(35,\cdot)$ $\chi_{7488}(107,\cdot)$ $\chi_{7488}(971,\cdot)$ $\chi_{7488}(1043,\cdot)$ $\chi_{7488}(1907,\cdot)$ $\chi_{7488}(1979,\cdot)$ $\chi_{7488}(2843,\cdot)$ $\chi_{7488}(2915,\cdot)$ $\chi_{7488}(3779,\cdot)$ $\chi_{7488}(3851,\cdot)$ $\chi_{7488}(4715,\cdot)$ $\chi_{7488}(4787,\cdot)$ $\chi_{7488}(5651,\cdot)$ $\chi_{7488}(5723,\cdot)$ $\chi_{7488}(6587,\cdot)$ $\chi_{7488}(6659,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{48})$
Fixed field:	Number field defined by a degree 48 polynomial

Values on generators

$(703,6085,5825,5761)$ → $(-1,e\left(\frac{1}{16}\right),-1,e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{ 7488 }(6587, a)$	$1$	$1$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{41}{48}\right)$	$1$	$e\left(\frac{1}{48}\right)$