Dirichlet character χ6384(3125,⋅)\chi_{6384}(3125,\cdot)

• Label: 6384.3125
• Modulus: $6384$
• Conductor: $6384$
• Order: $36$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$6384$
Conductor:	$6384$
Order:	$36$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 6384.of

$\chi_{6384}(5,\cdot)$ $\chi_{6384}(101,\cdot)$ $\chi_{6384}(1277,\cdot)$ $\chi_{6384}(1517,\cdot)$ $\chi_{6384}(2525,\cdot)$ $\chi_{6384}(3125,\cdot)$ $\chi_{6384}(3197,\cdot)$ $\chi_{6384}(3293,\cdot)$ $\chi_{6384}(4469,\cdot)$ $\chi_{6384}(4709,\cdot)$ $\chi_{6384}(5717,\cdot)$ $\chi_{6384}(6317,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	Number field defined by a degree 36 polynomial

Values on generators

$(799,4789,2129,913,1009)$ → $(1,i,-1,e\left(\frac{1}{6}\right),e\left(\frac{4}{9}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{ 6384 }(3125, a)$	$1$	$1$	$e\left(\frac{25}{36}\right)$	$-i$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{18}\right)$