Dirichlet character χ2548(1907,⋅)\chi_{2548}(1907,\cdot)

• Label: 2548.1907
• Modulus: $2548$
• Conductor: $2548$
• Order: $42$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2548$
Conductor:	$2548$
Order:	$42$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2548.dp

$\chi_{2548}(87,\cdot)$ $\chi_{2548}(159,\cdot)$ $\chi_{2548}(451,\cdot)$ $\chi_{2548}(523,\cdot)$ $\chi_{2548}(887,\cdot)$ $\chi_{2548}(1179,\cdot)$ $\chi_{2548}(1251,\cdot)$ $\chi_{2548}(1543,\cdot)$ $\chi_{2548}(1615,\cdot)$ $\chi_{2548}(1907,\cdot)$ $\chi_{2548}(2271,\cdot)$ $\chi_{2548}(2343,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{21})$
Fixed field:	Number field defined by a degree 42 polynomial

Values on generators

$(1275,885,197)$ → $(-1,e\left(\frac{31}{42}\right),e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$15$	$17$	$19$	$23$	$25$	$27$
$\chi_{ 2548 }(1907, a)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{17}{42}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{14}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{5}{7}\right)$