Dirichlet character χ1920(629,⋅)\chi_{1920}(629,\cdot)

• Label: 1920.629
• Modulus: $1920$
• Conductor: $1920$
• Order: $32$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1920$
Conductor:	$1920$
Order:	$32$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1920.db

$\chi_{1920}(29,\cdot)$ $\chi_{1920}(149,\cdot)$ $\chi_{1920}(269,\cdot)$ $\chi_{1920}(389,\cdot)$ $\chi_{1920}(509,\cdot)$ $\chi_{1920}(629,\cdot)$ $\chi_{1920}(749,\cdot)$ $\chi_{1920}(869,\cdot)$ $\chi_{1920}(989,\cdot)$ $\chi_{1920}(1109,\cdot)$ $\chi_{1920}(1229,\cdot)$ $\chi_{1920}(1349,\cdot)$ $\chi_{1920}(1469,\cdot)$ $\chi_{1920}(1589,\cdot)$ $\chi_{1920}(1709,\cdot)$ $\chi_{1920}(1829,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{32})$
Fixed field:	32.0.20615283744186880032112588280912120153429260426382010514145280000000000000000.1

Values on generators

$(511,901,641,1537)$ → $(1,e\left(\frac{21}{32}\right),-1,-1)$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 1920 }(629, a)$	$-1$	$1$	$e\left(\frac{1}{16}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{7}{32}\right)$	$i$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{3}{16}\right)$