Dirichlet character χ3700(1009,⋅)\chi_{3700}(1009,\cdot)

• Label: 3700.1009
• Modulus: $3700$
• Conductor: $925$
• Order: $30$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$3700$
Conductor:	$925$
Order:	$30$
Real:	no
Primitive:	no, induced from $\chi_{925}(84,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 3700.cr

$\chi_{3700}(269,\cdot)$ $\chi_{3700}(729,\cdot)$ $\chi_{3700}(1009,\cdot)$ $\chi_{3700}(1469,\cdot)$ $\chi_{3700}(2209,\cdot)$ $\chi_{3700}(2489,\cdot)$ $\chi_{3700}(3229,\cdot)$ $\chi_{3700}(3689,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	Number field defined by a degree 30 polynomial

Values on generators

$(1851,1777,1001)$ → $(1,e\left(\frac{7}{10}\right),e\left(\frac{2}{3}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$19$	$21$	$23$	$27$
$\chi_{ 3700 }(1009, a)$	$1$	$1$	$e\left(\frac{7}{30}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{15}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{14}{15}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{7}{10}\right)$