Dirichlet character χ243675(17,⋅)\chi_{243675}(17,\cdot)

• Label: 243675.17
• Modulus: $243675$
• Conductor: $81225$
• Order: $3420$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$243675$
Conductor:	$81225$
Order:	$3420$
Real:	no
Primitive:	no, induced from $\chi_{81225}(54167,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 243675.bdt

$\chi_{243675}(17,\cdot)$ $\chi_{243675}(233,\cdot)$ $\chi_{243675}(1277,\cdot)$ $\chi_{243675}(1358,\cdot)$ $\chi_{243675}(1412,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{3420})$
Fixed field:	Number field defined by a degree 3420 polynomial (not computed)

Values on generators

$(36101,77977,129601)$ → $(e\left(\frac{5}{6}\right),e\left(\frac{13}{20}\right),e\left(\frac{113}{171}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$11$	$13$	$14$	$16$	$17$	$22$
$\chi_{ 243675 }(17, a)$	$1$	$1$	$e\left(\frac{493}{3420}\right)$	$e\left(\frac{493}{1710}\right)$	$e\left(\frac{161}{228}\right)$	$e\left(\frac{493}{1140}\right)$	$e\left(\frac{121}{190}\right)$	$e\left(\frac{1457}{3420}\right)$	$e\left(\frac{727}{855}\right)$	$e\left(\frac{493}{855}\right)$	$e\left(\frac{1009}{3420}\right)$	$e\left(\frac{2671}{3420}\right)$