Dirichlet character χ2548(2081,⋅)\chi_{2548}(2081,\cdot)

• Label: 2548.2081
• Modulus: $2548$
• Conductor: $49$
• Order: $21$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2548$
Conductor:	$49$
Order:	$21$
Real:	no
Primitive:	no, induced from $\chi_{49}(23,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 2548.cs

$\chi_{2548}(53,\cdot)$ $\chi_{2548}(261,\cdot)$ $\chi_{2548}(417,\cdot)$ $\chi_{2548}(625,\cdot)$ $\chi_{2548}(781,\cdot)$ $\chi_{2548}(989,\cdot)$ $\chi_{2548}(1509,\cdot)$ $\chi_{2548}(1717,\cdot)$ $\chi_{2548}(1873,\cdot)$ $\chi_{2548}(2081,\cdot)$ $\chi_{2548}(2237,\cdot)$ $\chi_{2548}(2445,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 21 polynomial

Values on generators

$(1275,885,197)$ → $(1,e\left(\frac{19}{21}\right),1)$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{ 2548 }(2081, a)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{7}\right)$