Dirichlet character χ1710(193,⋅)\chi_{1710}(193,\cdot)

• Label: 1710.193
• 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 $\chi_{855}(193,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 1710.dq

$\chi_{1710}(193,\cdot)$ $\chi_{1710}(337,\cdot)$ $\chi_{1710}(547,\cdot)$ $\chi_{1710}(553,\cdot)$ $\chi_{1710}(583,\cdot)$ $\chi_{1710}(637,\cdot)$ $\chi_{1710}(877,\cdot)$ $\chi_{1710}(1237,\cdot)$ $\chi_{1710}(1267,\cdot)$ $\chi_{1710}(1363,\cdot)$ $\chi_{1710}(1573,\cdot)$ $\chi_{1710}(1663,\cdot)$

Related number fields

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

Values on generators

$(191,1027,1351)$ → $(e\left(\frac{1}{3}\right),-i,e\left(\frac{13}{18}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$23$	$29$	$31$	$37$	$41$	$43$
$\chi_{ 1710 }(193, a)$	$1$	$1$	$e\left(\frac{5}{12}\right)$	$1$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{9}\right)$	$-1$	$i$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{5}{36}\right)$