Dirichlet character χ3800(1531,⋅)\chi_{3800}(1531,\cdot)

• Label: 3800.1531
• 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.dt

$\chi_{3800}(11,\cdot)$ $\chi_{3800}(691,\cdot)$ $\chi_{3800}(771,\cdot)$ $\chi_{3800}(1531,\cdot)$ $\chi_{3800}(2211,\cdot)$ $\chi_{3800}(2291,\cdot)$ $\chi_{3800}(2971,\cdot)$ $\chi_{3800}(3731,\cdot)$

Related number fields

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

Values on generators

$(951,1901,1977,401)$ → $(-1,-1,e\left(\frac{2}{5}\right),e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3800 }(1531, a)$	$-1$	$1$	$e\left(\frac{7}{15}\right)$	$-1$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{30}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{19}{30}\right)$