Dirichlet character χ2656(47,⋅)\chi_{2656}(47,\cdot)

• Label: 2656.47
• Modulus: $2656$
• Conductor: $664$
• Order: $82$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$2656$
Conductor:	$664$
Order:	$82$
Real:	no
Primitive:	no, induced from $\chi_{664}(379,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 2656.r

$\chi_{2656}(15,\cdot)$ $\chi_{2656}(47,\cdot)$ $\chi_{2656}(79,\cdot)$ $\chi_{2656}(143,\cdot)$ $\chi_{2656}(239,\cdot)$ $\chi_{2656}(271,\cdot)$ $\chi_{2656}(303,\cdot)$ $\chi_{2656}(367,\cdot)$ $\chi_{2656}(399,\cdot)$ $\chi_{2656}(495,\cdot)$ $\chi_{2656}(623,\cdot)$ $\chi_{2656}(655,\cdot)$ $\chi_{2656}(719,\cdot)$ $\chi_{2656}(975,\cdot)$ $\chi_{2656}(1039,\cdot)$ $\chi_{2656}(1103,\cdot)$ $\chi_{2656}(1135,\cdot)$ $\chi_{2656}(1167,\cdot)$ $\chi_{2656}(1263,\cdot)$ $\chi_{2656}(1295,\cdot)$ $\chi_{2656}(1487,\cdot)$ $\chi_{2656}(1551,\cdot)$ $\chi_{2656}(1583,\cdot)$ $\chi_{2656}(1679,\cdot)$ $\chi_{2656}(1775,\cdot)$ $\chi_{2656}(1839,\cdot)$ $\chi_{2656}(1871,\cdot)$ $\chi_{2656}(1967,\cdot)$ $\chi_{2656}(2031,\cdot)$ $\chi_{2656}(2063,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{41})$
Fixed field:	Number field defined by a degree 82 polynomial

Values on generators

$(831,997,417)$ → $(-1,-1,e\left(\frac{23}{82}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 2656 }(47, a)$	$1$	$1$	$e\left(\frac{8}{41}\right)$	$e\left(\frac{3}{41}\right)$	$e\left(\frac{61}{82}\right)$	$e\left(\frac{16}{41}\right)$	$e\left(\frac{30}{41}\right)$	$e\left(\frac{4}{41}\right)$	$e\left(\frac{11}{41}\right)$	$e\left(\frac{29}{41}\right)$	$e\left(\frac{15}{82}\right)$	$e\left(\frac{77}{82}\right)$