Dirichlet character χ3800(289,⋅)\chi_{3800}(289,\cdot)

• Label: 3800.289
• Modulus: $3800$
• Conductor: $475$
• Order: $90$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3800$
Conductor:	$475$
Order:	$90$
Real:	no
Primitive:	no, induced from $\chi_{475}(289,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 3800.fd

$\chi_{3800}(9,\cdot)$ $\chi_{3800}(169,\cdot)$ $\chi_{3800}(289,\cdot)$ $\chi_{3800}(329,\cdot)$ $\chi_{3800}(529,\cdot)$ $\chi_{3800}(689,\cdot)$ $\chi_{3800}(769,\cdot)$ $\chi_{3800}(929,\cdot)$ $\chi_{3800}(1089,\cdot)$ $\chi_{3800}(1289,\cdot)$ $\chi_{3800}(1529,\cdot)$ $\chi_{3800}(1689,\cdot)$ $\chi_{3800}(1809,\cdot)$ $\chi_{3800}(2209,\cdot)$ $\chi_{3800}(2289,\cdot)$ $\chi_{3800}(2569,\cdot)$ $\chi_{3800}(2609,\cdot)$ $\chi_{3800}(2809,\cdot)$ $\chi_{3800}(2969,\cdot)$ $\chi_{3800}(3209,\cdot)$ $\chi_{3800}(3329,\cdot)$ $\chi_{3800}(3369,\cdot)$ $\chi_{3800}(3569,\cdot)$ $\chi_{3800}(3729,\cdot)$

Related number fields

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

Values on generators

$(951,1901,1977,401)$ → $(1,1,e\left(\frac{3}{10}\right),e\left(\frac{1}{9}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3800 }(289, a)$	$1$	$1$	$e\left(\frac{49}{90}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{45}\right)$	$e\left(\frac{2}{15}\right)$	$e\left(\frac{23}{90}\right)$	$e\left(\frac{1}{90}\right)$	$e\left(\frac{32}{45}\right)$	$e\left(\frac{47}{90}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{22}{45}\right)$