Dirichlet character χ3800(2111,⋅)\chi_{3800}(2111,\cdot)

• Label: 3800.2111
• Modulus: $3800$
• Conductor: $1900$
• Order: $90$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$3800$
Conductor:	$1900$
Order:	$90$
Real:	no
Primitive:	no, induced from $\chi_{1900}(211,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 3800.fb

$\chi_{3800}(71,\cdot)$ $\chi_{3800}(231,\cdot)$ $\chi_{3800}(431,\cdot)$ $\chi_{3800}(471,\cdot)$ $\chi_{3800}(591,\cdot)$ $\chi_{3800}(831,\cdot)$ $\chi_{3800}(991,\cdot)$ $\chi_{3800}(1191,\cdot)$ $\chi_{3800}(1231,\cdot)$ $\chi_{3800}(1511,\cdot)$ $\chi_{3800}(1591,\cdot)$ $\chi_{3800}(1991,\cdot)$ $\chi_{3800}(2111,\cdot)$ $\chi_{3800}(2271,\cdot)$ $\chi_{3800}(2511,\cdot)$ $\chi_{3800}(2711,\cdot)$ $\chi_{3800}(2871,\cdot)$ $\chi_{3800}(3031,\cdot)$ $\chi_{3800}(3111,\cdot)$ $\chi_{3800}(3271,\cdot)$ $\chi_{3800}(3471,\cdot)$ $\chi_{3800}(3511,\cdot)$ $\chi_{3800}(3631,\cdot)$ $\chi_{3800}(3791,\cdot)$

Related number fields

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

Values on generators

$(951,1901,1977,401)$ → $(-1,1,e\left(\frac{4}{5}\right),e\left(\frac{1}{18}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3800 }(2111, a)$	$1$	$1$	$e\left(\frac{37}{45}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{45}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{43}{90}\right)$	$e\left(\frac{43}{45}\right)$	$e\left(\frac{59}{90}\right)$	$e\left(\frac{37}{90}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{49}{90}\right)$