Dirichlet character χ2240(1949,⋅)\chi_{2240}(1949,\cdot)

• Label: 2240.1949
• Modulus: $2240$
• Conductor: $2240$
• Order: $48$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$2240$
Conductor:	$2240$
Order:	$48$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2240.ff

$\chi_{2240}(229,\cdot)$ $\chi_{2240}(269,\cdot)$ $\chi_{2240}(509,\cdot)$ $\chi_{2240}(549,\cdot)$ $\chi_{2240}(789,\cdot)$ $\chi_{2240}(829,\cdot)$ $\chi_{2240}(1069,\cdot)$ $\chi_{2240}(1109,\cdot)$ $\chi_{2240}(1349,\cdot)$ $\chi_{2240}(1389,\cdot)$ $\chi_{2240}(1629,\cdot)$ $\chi_{2240}(1669,\cdot)$ $\chi_{2240}(1909,\cdot)$ $\chi_{2240}(1949,\cdot)$ $\chi_{2240}(2189,\cdot)$ $\chi_{2240}(2229,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{48})$
Fixed field:	Number field defined by a degree 48 polynomial

Values on generators

$(1471,1541,897,1921)$ → $(1,e\left(\frac{11}{16}\right),-1,e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$3$	$9$	$11$	$13$	$17$	$19$	$23$	$27$	$29$	$31$
$\chi_{ 2240 }(1949, a)$	$-1$	$1$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{5}{16}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{2}{3}\right)$