Dirichlet character χ8788(6999,⋅)\chi_{8788}(6999,\cdot)

• Label: 8788.6999
• Modulus: $8788$
• Conductor: $676$
• Order: $52$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$8788$
Conductor:	$676$
Order:	$52$
Real:	no
Primitive:	no, induced from $\chi_{676}(83,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 8788.s

$\chi_{8788}(99,\cdot)$ $\chi_{8788}(775,\cdot)$ $\chi_{8788}(915,\cdot)$ $\chi_{8788}(1451,\cdot)$ $\chi_{8788}(1591,\cdot)$ $\chi_{8788}(2127,\cdot)$ $\chi_{8788}(2267,\cdot)$ $\chi_{8788}(2803,\cdot)$ $\chi_{8788}(2943,\cdot)$ $\chi_{8788}(3479,\cdot)$ $\chi_{8788}(3619,\cdot)$ $\chi_{8788}(4295,\cdot)$ $\chi_{8788}(4831,\cdot)$ $\chi_{8788}(4971,\cdot)$ $\chi_{8788}(5507,\cdot)$ $\chi_{8788}(5647,\cdot)$ $\chi_{8788}(6183,\cdot)$ $\chi_{8788}(6323,\cdot)$ $\chi_{8788}(6859,\cdot)$ $\chi_{8788}(6999,\cdot)$ $\chi_{8788}(7535,\cdot)$ $\chi_{8788}(7675,\cdot)$ $\chi_{8788}(8211,\cdot)$ $\chi_{8788}(8351,\cdot)$

Related number fields

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

Values on generators

$(4395,6593)$ → $(-1,e\left(\frac{15}{52}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 8788 }(6999, a)$	$1$	$1$	$e\left(\frac{7}{26}\right)$	$e\left(\frac{31}{52}\right)$	$e\left(\frac{19}{52}\right)$	$e\left(\frac{7}{13}\right)$	$e\left(\frac{11}{52}\right)$	$e\left(\frac{45}{52}\right)$	$e\left(\frac{3}{26}\right)$	$i$	$e\left(\frac{33}{52}\right)$	$1$