Dirichlet character χ1520(1219,⋅)\chi_{1520}(1219,\cdot)

• Label: 1520.1219
• Modulus: $1520$
• Conductor: $1520$
• Order: $36$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1520$
Conductor:	$1520$
Order:	$36$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1520.en

$\chi_{1520}(59,\cdot)$ $\chi_{1520}(219,\cdot)$ $\chi_{1520}(299,\cdot)$ $\chi_{1520}(459,\cdot)$ $\chi_{1520}(659,\cdot)$ $\chi_{1520}(699,\cdot)$ $\chi_{1520}(819,\cdot)$ $\chi_{1520}(979,\cdot)$ $\chi_{1520}(1059,\cdot)$ $\chi_{1520}(1219,\cdot)$ $\chi_{1520}(1419,\cdot)$ $\chi_{1520}(1459,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	Number field defined by a degree 36 polynomial

Values on generators

$(191,1141,1217,401)$ → $(-1,-i,-1,e\left(\frac{13}{18}\right))$

First values

$a$	$-1$	$1$	$3$	$7$	$9$	$11$	$13$	$17$	$21$	$23$	$27$	$29$
$\chi_{ 1520 }(1219, a)$	$1$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{19}{36}\right)$