Dirichlet character χ3800(69,⋅)\chi_{3800}(69,\cdot)

• Label: 3800.69
• Modulus: $3800$
• Conductor: $3800$
• Order: $30$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3800$
Conductor:	$3800$
Order:	$30$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 3800.dn

$\chi_{3800}(69,\cdot)$ $\chi_{3800}(829,\cdot)$ $\chi_{3800}(1509,\cdot)$ $\chi_{3800}(1589,\cdot)$ $\chi_{3800}(2269,\cdot)$ $\chi_{3800}(3029,\cdot)$ $\chi_{3800}(3109,\cdot)$ $\chi_{3800}(3789,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	Number field defined by a degree 30 polynomial

Values on generators

$(951,1901,1977,401)$ → $(1,-1,e\left(\frac{9}{10}\right),e\left(\frac{5}{6}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3800 }(69, a)$	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$-1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{9}{10}\right)$	$e\left(\frac{7}{15}\right)$