Dirichlet character χ7448(3649,⋅)\chi_{7448}(3649,\cdot)

• Label: 7448.3649
• Modulus: $7448$
• Conductor: $49$
• Order: $21$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$7448$
Conductor:	$49$
Order:	$21$
Real:	no
Primitive:	no, induced from $\chi_{49}(23,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 7448.fr

$\chi_{7448}(305,\cdot)$ $\chi_{7448}(457,\cdot)$ $\chi_{7448}(1369,\cdot)$ $\chi_{7448}(1521,\cdot)$ $\chi_{7448}(2433,\cdot)$ $\chi_{7448}(2585,\cdot)$ $\chi_{7448}(3649,\cdot)$ $\chi_{7448}(4561,\cdot)$ $\chi_{7448}(4713,\cdot)$ $\chi_{7448}(5625,\cdot)$ $\chi_{7448}(5777,\cdot)$ $\chi_{7448}(6689,\cdot)$

Related number fields

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

Values on generators

$(1863,3725,3041,3137)$ → $(1,1,e\left(\frac{19}{21}\right),1)$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$23$	$25$	$27$
$\chi_{ 7448 }(3649, a)$	$1$	$1$	$e\left(\frac{19}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{17}{21}\right)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{6}{7}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{10}{21}\right)$	$e\left(\frac{5}{7}\right)$