Dirichlet character χ2704(1919,⋅)\chi_{2704}(1919,\cdot)

• Label: 2704.1919
• Modulus: $2704$
• Conductor: $676$
• Order: $52$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2704$
Conductor:	$676$
Order:	$52$
Real:	no
Primitive:	no, induced from $\chi_{676}(567,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 2704.ci

$\chi_{2704}(31,\cdot)$ $\chi_{2704}(47,\cdot)$ $\chi_{2704}(255,\cdot)$ $\chi_{2704}(447,\cdot)$ $\chi_{2704}(463,\cdot)$ $\chi_{2704}(655,\cdot)$ $\chi_{2704}(671,\cdot)$ $\chi_{2704}(863,\cdot)$ $\chi_{2704}(879,\cdot)$ $\chi_{2704}(1071,\cdot)$ $\chi_{2704}(1087,\cdot)$ $\chi_{2704}(1279,\cdot)$ $\chi_{2704}(1295,\cdot)$ $\chi_{2704}(1487,\cdot)$ $\chi_{2704}(1503,\cdot)$ $\chi_{2704}(1695,\cdot)$ $\chi_{2704}(1711,\cdot)$ $\chi_{2704}(1903,\cdot)$ $\chi_{2704}(1919,\cdot)$ $\chi_{2704}(2111,\cdot)$ $\chi_{2704}(2319,\cdot)$ $\chi_{2704}(2335,\cdot)$ $\chi_{2704}(2527,\cdot)$ $\chi_{2704}(2543,\cdot)$

Related number fields

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

Values on generators

$(2367,677,1185)$ → $(-1,1,e\left(\frac{45}{52}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 2704 }(1919, a)$	$1$	$1$	$e\left(\frac{21}{26}\right)$	$e\left(\frac{41}{52}\right)$	$e\left(\frac{5}{52}\right)$	$e\left(\frac{8}{13}\right)$	$e\left(\frac{33}{52}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{9}{26}\right)$	$-i$	$e\left(\frac{47}{52}\right)$	$1$