Dirichlet character χ7448(2003,⋅)\chi_{7448}(2003,\cdot)

• Label: 7448.2003
• Modulus: $7448$
• Conductor: $7448$
• Order: $42$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$7448$
Conductor:	$7448$
Order:	$42$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 7448.ge

$\chi_{7448}(715,\cdot)$ $\chi_{7448}(939,\cdot)$ $\chi_{7448}(1779,\cdot)$ $\chi_{7448}(2003,\cdot)$ $\chi_{7448}(3067,\cdot)$ $\chi_{7448}(3907,\cdot)$ $\chi_{7448}(4131,\cdot)$ $\chi_{7448}(4971,\cdot)$ $\chi_{7448}(6035,\cdot)$ $\chi_{7448}(6259,\cdot)$ $\chi_{7448}(7099,\cdot)$ $\chi_{7448}(7323,\cdot)$

Related number fields

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

Values on generators

$(1863,3725,3041,3137)$ → $(-1,-1,e\left(\frac{1}{7}\right),e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$23$	$25$	$27$
$\chi_{ 7448 }(2003, a)$	$1$	$1$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{7}\right)$	$e\left(\frac{1}{21}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{5}{21}\right)$	$e\left(\frac{11}{42}\right)$	$e\left(\frac{13}{21}\right)$	$e\left(\frac{13}{14}\right)$