Dirichlet character χ3800(629,⋅)\chi_{3800}(629,\cdot)

• Label: 3800.629
• 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.ez

$\chi_{3800}(29,\cdot)$ $\chi_{3800}(109,\cdot)$ $\chi_{3800}(269,\cdot)$ $\chi_{3800}(469,\cdot)$ $\chi_{3800}(509,\cdot)$ $\chi_{3800}(629,\cdot)$ $\chi_{3800}(789,\cdot)$ $\chi_{3800}(869,\cdot)$ $\chi_{3800}(1029,\cdot)$ $\chi_{3800}(1229,\cdot)$ $\chi_{3800}(1269,\cdot)$ $\chi_{3800}(1389,\cdot)$ $\chi_{3800}(1629,\cdot)$ $\chi_{3800}(1789,\cdot)$ $\chi_{3800}(1989,\cdot)$ $\chi_{3800}(2029,\cdot)$ $\chi_{3800}(2309,\cdot)$ $\chi_{3800}(2389,\cdot)$ $\chi_{3800}(2789,\cdot)$ $\chi_{3800}(2909,\cdot)$ $\chi_{3800}(3069,\cdot)$ $\chi_{3800}(3309,\cdot)$ $\chi_{3800}(3509,\cdot)$ $\chi_{3800}(3669,\cdot)$

Related number fields

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

Values on generators

$(951,1901,1977,401)$ → $(1,-1,e\left(\frac{1}{10}\right),e\left(\frac{1}{18}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3800 }(629, a)$	$-1$	$1$	$e\left(\frac{83}{90}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{38}{45}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{61}{90}\right)$	$e\left(\frac{77}{90}\right)$	$e\left(\frac{34}{45}\right)$	$e\left(\frac{19}{90}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{29}{45}\right)$