Dirichlet character χ3800(2419,⋅)\chi_{3800}(2419,\cdot)

• Label: 3800.2419
• Modulus: $3800$
• Conductor: $3800$
• Order: $90$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3800$
Conductor:	$3800$
Order:	$90$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 3800.ev

$\chi_{3800}(139,\cdot)$ $\chi_{3800}(339,\cdot)$ $\chi_{3800}(579,\cdot)$ $\chi_{3800}(739,\cdot)$ $\chi_{3800}(859,\cdot)$ $\chi_{3800}(1259,\cdot)$ $\chi_{3800}(1339,\cdot)$ $\chi_{3800}(1619,\cdot)$ $\chi_{3800}(1659,\cdot)$ $\chi_{3800}(1859,\cdot)$ $\chi_{3800}(2019,\cdot)$ $\chi_{3800}(2259,\cdot)$ $\chi_{3800}(2379,\cdot)$ $\chi_{3800}(2419,\cdot)$ $\chi_{3800}(2619,\cdot)$ $\chi_{3800}(2779,\cdot)$ $\chi_{3800}(2859,\cdot)$ $\chi_{3800}(3019,\cdot)$ $\chi_{3800}(3139,\cdot)$ $\chi_{3800}(3179,\cdot)$ $\chi_{3800}(3379,\cdot)$ $\chi_{3800}(3539,\cdot)$ $\chi_{3800}(3619,\cdot)$ $\chi_{3800}(3779,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{45})$
Fixed field:	Number field defined by a degree 90 polynomial

Values on generators

$(951,1901,1977,401)$ → $(-1,-1,e\left(\frac{9}{10}\right),e\left(\frac{7}{9}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3800 }(2419, a)$	$-1$	$1$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{22}{45}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{7}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{47}{90}\right)$