Dirichlet character χ6384(1187,⋅)\chi_{6384}(1187,\cdot)

• Label: 6384.1187
• 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.og

$\chi_{6384}(947,\cdot)$ $\chi_{6384}(1187,\cdot)$ $\chi_{6384}(1355,\cdot)$ $\chi_{6384}(1955,\cdot)$ $\chi_{6384}(2531,\cdot)$ $\chi_{6384}(2627,\cdot)$ $\chi_{6384}(4139,\cdot)$ $\chi_{6384}(4379,\cdot)$ $\chi_{6384}(4547,\cdot)$ $\chi_{6384}(5147,\cdot)$ $\chi_{6384}(5723,\cdot)$ $\chi_{6384}(5819,\cdot)$

Related number fields

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

Values on generators

$(799,4789,2129,913,1009)$ → $(-1,-i,-1,e\left(\frac{2}{3}\right),e\left(\frac{4}{9}\right))$

First values

$a$	$-1$	$1$	$5$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$37$	$41$
$\chi_{ 6384 }(1187, a)$	$1$	$1$	$e\left(\frac{25}{36}\right)$	$-i$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{9}\right)$