Dirichlet character χ3800(3107,⋅)\chi_{3800}(3107,\cdot)

• Label: 3800.3107
• Modulus: $3800$
• Conductor: $760$
• Order: $36$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3800$
Conductor:	$760$
Order:	$36$
Real:	no
Primitive:	no, induced from $\chi_{760}(67,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 3800.eb

$\chi_{3800}(243,\cdot)$ $\chi_{3800}(307,\cdot)$ $\chi_{3800}(507,\cdot)$ $\chi_{3800}(907,\cdot)$ $\chi_{3800}(1307,\cdot)$ $\chi_{3800}(2043,\cdot)$ $\chi_{3800}(2643,\cdot)$ $\chi_{3800}(3043,\cdot)$ $\chi_{3800}(3107,\cdot)$ $\chi_{3800}(3243,\cdot)$ $\chi_{3800}(3643,\cdot)$ $\chi_{3800}(3707,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	36.0.4031181156993454136731178943694064571490658196389888000000000000000000000000000.1

Values on generators

$(951,1901,1977,401)$ → $(-1,-1,i,e\left(\frac{17}{18}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 3800 }(3107, a)$	$-1$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{18}\right)$