Dirichlet character χ7448(649,⋅)\chi_{7448}(649,\cdot)

• Label: 7448.649
• Modulus: $7448$
• Conductor: $931$
• Order: $126$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$7448$
Conductor:	$931$
Order:	$126$
Real:	no
Primitive:	no, induced from $\chi_{931}(649,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 7448.ih

$\chi_{7448}(33,\cdot)$ $\chi_{7448}(241,\cdot)$ $\chi_{7448}(409,\cdot)$ $\chi_{7448}(649,\cdot)$ $\chi_{7448}(1193,\cdot)$ $\chi_{7448}(1473,\cdot)$ $\chi_{7448}(1713,\cdot)$ $\chi_{7448}(1769,\cdot)$ $\chi_{7448}(2161,\cdot)$ $\chi_{7448}(2257,\cdot)$ $\chi_{7448}(2369,\cdot)$ $\chi_{7448}(2537,\cdot)$ $\chi_{7448}(2777,\cdot)$ $\chi_{7448}(2833,\cdot)$ $\chi_{7448}(3225,\cdot)$ $\chi_{7448}(3321,\cdot)$ $\chi_{7448}(3433,\cdot)$ $\chi_{7448}(3601,\cdot)$ $\chi_{7448}(3897,\cdot)$ $\chi_{7448}(4289,\cdot)$ $\chi_{7448}(4385,\cdot)$ $\chi_{7448}(4497,\cdot)$ $\chi_{7448}(4665,\cdot)$ $\chi_{7448}(4905,\cdot)$ $\chi_{7448}(4961,\cdot)$ $\chi_{7448}(5353,\cdot)$ $\chi_{7448}(5449,\cdot)$ $\chi_{7448}(5561,\cdot)$ $\chi_{7448}(5729,\cdot)$ $\chi_{7448}(5969,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{63})$
Fixed field:	Number field defined by a degree 126 polynomial (not computed)

Values on generators

$(1863,3725,3041,3137)$ → $(1,1,e\left(\frac{11}{42}\right),e\left(\frac{13}{18}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$23$	$25$	$27$
$\chi_{ 7448 }(649, a)$	$1$	$1$	$e\left(\frac{41}{63}\right)$	$e\left(\frac{19}{126}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{16}{63}\right)$	$e\left(\frac{101}{126}\right)$	$e\left(\frac{97}{126}\right)$	$e\left(\frac{25}{63}\right)$	$e\left(\frac{19}{63}\right)$	$e\left(\frac{20}{21}\right)$