Dirichlet character orbit 1710.dq

• Label: 1710.dq
• Modulus: $1710$
• Conductor: $855$
• Order: $36$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1710$
Conductor:	$855$
Order:	$36$
Real:	no
Primitive:	no, induced from 855.dq
Minimal:	yes
Parity:	even

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	36.36.17849776228866488737715206984999102954438314099226129130939288096733391284942626953125.1

Characters in Galois orbit

Character	$-1$	$1$	$7$	$11$	$13$	$17$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{1710}(193,\cdot)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{9}\right)$	$-1$	$i$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{36}\right)$
$\chi_{1710}(337,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{4}{9}\right)$	$-1$	$-i$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{11}{36}\right)$
$\chi_{1710}(547,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{5}{9}\right)$	$-1$	$-i$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{7}{36}\right)$
$\chi_{1710}(553,\cdot)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{7}{9}\right)$	$-1$	$i$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{17}{36}\right)$
$\chi_{1710}(583,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{8}{9}\right)$	$-1$	$i$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{13}{36}\right)$
$\chi_{1710}(637,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{2}{9}\right)$	$-1$	$-i$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{19}{36}\right)$
$\chi_{1710}(877,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{1}{9}\right)$	$-1$	$-i$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{23}{36}\right)$
$\chi_{1710}(1237,\cdot)$	$1$	$1$	$e\left(\frac{11}{12}\right)$	$1$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{9}\right)$	$-1$	$-i$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{35}{36}\right)$
$\chi_{1710}(1267,\cdot)$	$1$	$1$	$e\left(\frac{7}{12}\right)$	$1$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{8}{9}\right)$	$-1$	$-i$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{31}{36}\right)$
$\chi_{1710}(1363,\cdot)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{4}{9}\right)$	$-1$	$i$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{29}{36}\right)$
$\chi_{1710}(1573,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{9}\right)$	$-1$	$i$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{25}{36}\right)$
$\chi_{1710}(1663,\cdot)$	$1$	$1$	$e\left(\frac{1}{12}\right)$	$1$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{2}{9}\right)$	$-1$	$i$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{36}\right)$