Dirichlet character χ7920(2713,⋅)\chi_{7920}(2713,\cdot)

• Label: 7920.2713
• Modulus: $7920$
• Conductor: $3960$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$7920$
Conductor:	$3960$
Order:	$60$
Real:	no
Primitive:	no, induced from $\chi_{3960}(733,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 7920.lm

$\chi_{7920}(457,\cdot)$ $\chi_{7920}(1273,\cdot)$ $\chi_{7920}(1993,\cdot)$ $\chi_{7920}(2713,\cdot)$ $\chi_{7920}(2857,\cdot)$ $\chi_{7920}(3577,\cdot)$ $\chi_{7920}(3913,\cdot)$ $\chi_{7920}(4153,\cdot)$ $\chi_{7920}(4297,\cdot)$ $\chi_{7920}(4633,\cdot)$ $\chi_{7920}(5353,\cdot)$ $\chi_{7920}(5497,\cdot)$ $\chi_{7920}(5737,\cdot)$ $\chi_{7920}(6217,\cdot)$ $\chi_{7920}(6793,\cdot)$ $\chi_{7920}(6937,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{60})$
Fixed field:	Number field defined by a degree 60 polynomial

Values on generators

$(991,5941,3521,6337,6481)$ → $(1,-1,e\left(\frac{1}{3}\right),-i,e\left(\frac{7}{10}\right))$

First values

$a$	$-1$	$1$	$7$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 7920 }(2713, a)$	$1$	$1$	$e\left(\frac{59}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{1}{20}\right)$	$e\left(\frac{1}{10}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{12}\right)$