Dirichlet character χ864(589,⋅)\chi_{864}(589,\cdot)

• Label: 864.589
• Modulus: $864$
• Conductor: $864$
• Order: $72$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$864$
Conductor:	$864$
Order:	$72$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 864.bu

$\chi_{864}(13,\cdot)$ $\chi_{864}(61,\cdot)$ $\chi_{864}(85,\cdot)$ $\chi_{864}(133,\cdot)$ $\chi_{864}(157,\cdot)$ $\chi_{864}(205,\cdot)$ $\chi_{864}(229,\cdot)$ $\chi_{864}(277,\cdot)$ $\chi_{864}(301,\cdot)$ $\chi_{864}(349,\cdot)$ $\chi_{864}(373,\cdot)$ $\chi_{864}(421,\cdot)$ $\chi_{864}(445,\cdot)$ $\chi_{864}(493,\cdot)$ $\chi_{864}(517,\cdot)$ $\chi_{864}(565,\cdot)$ $\chi_{864}(589,\cdot)$ $\chi_{864}(637,\cdot)$ $\chi_{864}(661,\cdot)$ $\chi_{864}(709,\cdot)$ $\chi_{864}(733,\cdot)$ $\chi_{864}(781,\cdot)$ $\chi_{864}(805,\cdot)$ $\chi_{864}(853,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{72})$
Fixed field:	Number field defined by a degree 72 polynomial

Values on generators

$(703,325,353)$ → $(1,e\left(\frac{7}{8}\right),e\left(\frac{7}{9}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{ 864 }(589, a)$	$1$	$1$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{5}{9}\right)$

Gauss sum

Jacobi sum

Kloosterman sum