Dirichlet character χ45120(20689,⋅)\chi_{45120}(20689,\cdot)

• Label: 45120.20689
• Modulus: $45120$
• Conductor: $3760$
• Order: $92$
• Real: no
• Primitive: no
• Minimal: no
• Parity: even

Basic properties

Modulus:	$45120$
Conductor:	$3760$
Order:	$92$
Real:	no
Primitive:	no, induced from $\chi_{3760}(2829,\cdot)$
Minimal:	no
Parity:	even

Galois orbit 45120.gy

$\chi_{45120}(49,\cdot)$ $\chi_{45120}(529,\cdot)$ $\chi_{45120}(1489,\cdot)$ $\chi_{45120}(1969,\cdot)$ $\chi_{45120}(3409,\cdot)$ $\chi_{45120}(4849,\cdot)$ $\chi_{45120}(5329,\cdot)$ $\chi_{45120}(5809,\cdot)$ $\chi_{45120}(7729,\cdot)$ $\chi_{45120}(9169,\cdot)$ $\chi_{45120}(9649,\cdot)$ $\chi_{45120}(10129,\cdot)$ $\chi_{45120}(10609,\cdot)$ $\chi_{45120}(11569,\cdot)$ $\chi_{45120}(12049,\cdot)$ $\chi_{45120}(12529,\cdot)$ $\chi_{45120}(13009,\cdot)$ $\chi_{45120}(15889,\cdot)$ $\chi_{45120}(18289,\cdot)$ $\chi_{45120}(18769,\cdot)$ $\chi_{45120}(19729,\cdot)$ $\chi_{45120}(20689,\cdot)$ $\chi_{45120}(22609,\cdot)$ $\chi_{45120}(23089,\cdot)$ $\chi_{45120}(24049,\cdot)$ $\chi_{45120}(24529,\cdot)$ $\chi_{45120}(25969,\cdot)$ $\chi_{45120}(27409,\cdot)$ $\chi_{45120}(27889,\cdot)$ $\chi_{45120}(28369,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{92})$
Fixed field:	Number field defined by a degree 92 polynomial

Values on generators

$(43711,2821,15041,36097,18241)$ → $(1,-i,1,-1,e\left(\frac{20}{23}\right))$

First values

$a$	$-1$	$1$	$7$	$11$	$13$	$17$	$19$	$23$	$29$	$31$	$37$	$41$
$\chi_{ 45120 }(20689, a)$	$1$	$1$	$e\left(\frac{19}{23}\right)$	$e\left(\frac{77}{92}\right)$	$e\left(\frac{29}{92}\right)$	$e\left(\frac{19}{46}\right)$	$e\left(\frac{35}{92}\right)$	$e\left(\frac{8}{23}\right)$	$e\left(\frac{63}{92}\right)$	$e\left(\frac{14}{23}\right)$	$e\left(\frac{71}{92}\right)$	$e\left(\frac{25}{46}\right)$