Dirichlet character χ8512(5219,⋅)\chi_{8512}(5219,\cdot)

• Label: 8512.5219
• Modulus: $8512$
• Conductor: $8512$
• Order: $144$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$8512$
Conductor:	$8512$
Order:	$144$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8512.md

$\chi_{8512}(67,\cdot)$ $\chi_{8512}(611,\cdot)$ $\chi_{8512}(667,\cdot)$ $\chi_{8512}(851,\cdot)$ $\chi_{8512}(963,\cdot)$ $\chi_{8512}(1059,\cdot)$ $\chi_{8512}(1131,\cdot)$ $\chi_{8512}(1675,\cdot)$ $\chi_{8512}(1731,\cdot)$ $\chi_{8512}(1915,\cdot)$ $\chi_{8512}(2027,\cdot)$ $\chi_{8512}(2123,\cdot)$ $\chi_{8512}(2195,\cdot)$ $\chi_{8512}(2739,\cdot)$ $\chi_{8512}(2795,\cdot)$ $\chi_{8512}(2979,\cdot)$ $\chi_{8512}(3091,\cdot)$ $\chi_{8512}(3187,\cdot)$ $\chi_{8512}(3259,\cdot)$ $\chi_{8512}(3803,\cdot)$ $\chi_{8512}(3859,\cdot)$ $\chi_{8512}(4043,\cdot)$ $\chi_{8512}(4155,\cdot)$ $\chi_{8512}(4251,\cdot)$ $\chi_{8512}(4323,\cdot)$ $\chi_{8512}(4867,\cdot)$ $\chi_{8512}(4923,\cdot)$ $\chi_{8512}(5107,\cdot)$ $\chi_{8512}(5219,\cdot)$ $\chi_{8512}(5315,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{144})$
Fixed field:	Number field defined by a degree 144 polynomial (not computed)

Values on generators

$(5055,6917,7297,3137)$ → $(-1,e\left(\frac{11}{16}\right),e\left(\frac{2}{3}\right),e\left(\frac{5}{18}\right))$

First values

$a$	$-1$	$1$	$3$	$5$	$9$	$11$	$13$	$15$	$17$	$23$	$25$	$27$
$\chi_{ 8512 }(5219, a)$	$1$	$1$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{25}{48}\right)$