Dirichlet character χ3660(2509,⋅)\chi_{3660}(2509,\cdot)

• Label: 3660.2509
• Modulus: $3660$
• Conductor: $305$
• Order: $20$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$3660$
Conductor:	$305$
Order:	$20$
Real:	no
Primitive:	no, induced from $\chi_{305}(69,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 3660.ee

$\chi_{3660}(709,\cdot)$ $\chi_{3660}(769,\cdot)$ $\chi_{3660}(1009,\cdot)$ $\chi_{3660}(1309,\cdot)$ $\chi_{3660}(1549,\cdot)$ $\chi_{3660}(1609,\cdot)$ $\chi_{3660}(2509,\cdot)$ $\chi_{3660}(3469,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{20})$
Fixed field:	20.0.81464220930404573824378260231257236328125.1

Values on generators

$(1831,2441,2197,3601)$ → $(1,1,-1,e\left(\frac{1}{20}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 3660 }(2509, a)$	$-1$	$1$	$e\left(\frac{19}{20}\right)$	$-i$	$-1$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{3}{10}\right)$	$e\left(\frac{7}{20}\right)$	$-i$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{7}{10}\right)$