Dirichlet character χ3800(27,⋅)\chi_{3800}(27,\cdot)

• Label: 3800.27
• Modulus: $3800$
• Conductor: $3800$
• Order: $60$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3800$
Conductor:	$3800$
Order:	$60$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 3800.el

$\chi_{3800}(27,\cdot)$ $\chi_{3800}(483,\cdot)$ $\chi_{3800}(563,\cdot)$ $\chi_{3800}(787,\cdot)$ $\chi_{3800}(867,\cdot)$ $\chi_{3800}(1323,\cdot)$ $\chi_{3800}(1547,\cdot)$ $\chi_{3800}(1627,\cdot)$ $\chi_{3800}(2003,\cdot)$ $\chi_{3800}(2083,\cdot)$ $\chi_{3800}(2387,\cdot)$ $\chi_{3800}(2763,\cdot)$ $\chi_{3800}(3067,\cdot)$ $\chi_{3800}(3147,\cdot)$ $\chi_{3800}(3523,\cdot)$ $\chi_{3800}(3603,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{60})$
Fixed field:	Number field defined by a degree 60 polynomial

Values on generators

$(951,1901,1977,401)$ → $(-1,-1,e\left(\frac{1}{20}\right),e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3800 }(27, a)$	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$-i$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{17}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{13}{30}\right)$