Dirichlet character χ3800(369,⋅)\chi_{3800}(369,\cdot)

• Label: 3800.369
• Modulus: $3800$
• Conductor: $475$
• Order: $30$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3800$
Conductor:	$475$
Order:	$30$
Real:	no
Primitive:	no, induced from $\chi_{475}(369,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 3800.du

$\chi_{3800}(369,\cdot)$ $\chi_{3800}(1129,\cdot)$ $\chi_{3800}(1209,\cdot)$ $\chi_{3800}(1889,\cdot)$ $\chi_{3800}(1969,\cdot)$ $\chi_{3800}(2729,\cdot)$ $\chi_{3800}(3409,\cdot)$ $\chi_{3800}(3489,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	30.0.41334267425810406820389890772071250779617912485264241695404052734375.1

Values on generators

$(951,1901,1977,401)$ → $(1,1,e\left(\frac{9}{10}\right),e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3800 }(369, a)$	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$-1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{11}{30}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{30}\right)$