Dirichlet character χ2028(473,⋅)\chi_{2028}(473,\cdot)

• Label: 2028.473
• Modulus: $2028$
• Conductor: $507$
• Order: $52$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2028$
Conductor:	$507$
Order:	$52$
Real:	no
Primitive:	no, induced from $\chi_{507}(473,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 2028.bi

$\chi_{2028}(5,\cdot)$ $\chi_{2028}(125,\cdot)$ $\chi_{2028}(161,\cdot)$ $\chi_{2028}(281,\cdot)$ $\chi_{2028}(317,\cdot)$ $\chi_{2028}(473,\cdot)$ $\chi_{2028}(593,\cdot)$ $\chi_{2028}(629,\cdot)$ $\chi_{2028}(749,\cdot)$ $\chi_{2028}(785,\cdot)$ $\chi_{2028}(905,\cdot)$ $\chi_{2028}(941,\cdot)$ $\chi_{2028}(1061,\cdot)$ $\chi_{2028}(1097,\cdot)$ $\chi_{2028}(1217,\cdot)$ $\chi_{2028}(1373,\cdot)$ $\chi_{2028}(1409,\cdot)$ $\chi_{2028}(1529,\cdot)$ $\chi_{2028}(1565,\cdot)$ $\chi_{2028}(1685,\cdot)$ $\chi_{2028}(1721,\cdot)$ $\chi_{2028}(1841,\cdot)$ $\chi_{2028}(1877,\cdot)$ $\chi_{2028}(1997,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Values on generators

$(1015,677,1861)$ → $(1,-1,e\left(\frac{23}{52}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{ 2028 }(473, a)$	$1$	$1$	$e\left(\frac{25}{52}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{13}\right)$	$-i$	$1$	$e\left(\frac{25}{26}\right)$	$e\left(\frac{5}{26}\right)$	$e\left(\frac{15}{52}\right)$	$e\left(\frac{21}{26}\right)$