Dirichlet character χ8788(8689,⋅)\chi_{8788}(8689,\cdot)

• Label: 8788.8689
• Modulus: $8788$
• Conductor: $169$
• Order: $52$
• Real: no
• Primitive: no
• Minimal: no
• Parity: odd

Basic properties

Modulus:	$8788$
Conductor:	$169$
Order:	$52$
Real:	no
Primitive:	no, induced from $\chi_{169}(44,\cdot)$
Minimal:	no
Parity:	odd

Galois orbit 8788.r

$\chi_{8788}(437,\cdot)$ $\chi_{8788}(577,\cdot)$ $\chi_{8788}(1113,\cdot)$ $\chi_{8788}(1253,\cdot)$ $\chi_{8788}(1789,\cdot)$ $\chi_{8788}(1929,\cdot)$ $\chi_{8788}(2465,\cdot)$ $\chi_{8788}(2605,\cdot)$ $\chi_{8788}(3141,\cdot)$ $\chi_{8788}(3281,\cdot)$ $\chi_{8788}(3817,\cdot)$ $\chi_{8788}(3957,\cdot)$ $\chi_{8788}(4493,\cdot)$ $\chi_{8788}(5169,\cdot)$ $\chi_{8788}(5309,\cdot)$ $\chi_{8788}(5845,\cdot)$ $\chi_{8788}(5985,\cdot)$ $\chi_{8788}(6521,\cdot)$ $\chi_{8788}(6661,\cdot)$ $\chi_{8788}(7197,\cdot)$ $\chi_{8788}(7337,\cdot)$ $\chi_{8788}(7873,\cdot)$ $\chi_{8788}(8013,\cdot)$ $\chi_{8788}(8689,\cdot)$

Related number fields

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

Values on generators

$(4395,6593)$ → $(1,e\left(\frac{35}{52}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$15$	$17$	$19$	$21$	$23$
$\chi_{ 8788 }(8689, a)$	$-1$	$1$	$e\left(\frac{6}{13}\right)$	$e\left(\frac{3}{52}\right)$	$e\left(\frac{1}{52}\right)$	$e\left(\frac{12}{13}\right)$	$e\left(\frac{17}{52}\right)$	$e\left(\frac{27}{52}\right)$	$e\left(\frac{7}{26}\right)$	$-i$	$e\left(\frac{25}{52}\right)$	$-1$