Dirichlet character χ9405(9007,⋅)\chi_{9405}(9007,\cdot)

• Label: 9405.9007
• Modulus: $9405$
• Conductor: $495$
• Order: $60$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$9405$
Conductor:	$495$
Order:	$60$
Real:	no
Primitive:	no, induced from $\chi_{495}(97,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 9405.lc

$\chi_{9405}(58,\cdot)$ $\chi_{9405}(742,\cdot)$ $\chi_{9405}(1312,\cdot)$ $\chi_{9405}(1483,\cdot)$ $\chi_{9405}(2623,\cdot)$ $\chi_{9405}(3193,\cdot)$ $\chi_{9405}(3877,\cdot)$ $\chi_{9405}(4162,\cdot)$ $\chi_{9405}(5758,\cdot)$ $\chi_{9405}(5872,\cdot)$ $\chi_{9405}(6043,\cdot)$ $\chi_{9405}(7297,\cdot)$ $\chi_{9405}(7582,\cdot)$ $\chi_{9405}(7753,\cdot)$ $\chi_{9405}(9007,\cdot)$ $\chi_{9405}(9178,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{60})$
Fixed field:	Number field defined by a degree 60 polynomial

Values on generators

$(1046,1882,5986,496)$ → $(e\left(\frac{2}{3}\right),i,e\left(\frac{3}{5}\right),1)$

First values

$a$	$-1$	$1$	$2$	$4$	$7$	$8$	$13$	$14$	$16$	$17$	$23$	$26$
$\chi_{ 9405 }(9007, a)$	$-1$	$1$	$e\left(\frac{31}{60}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{11}{20}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{15}\right)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{5}\right)$