Dirichlet character χ1254(653,⋅)\chi_{1254}(653,\cdot)

• Label: 1254.653
• Modulus: $1254$
• Conductor: $627$
• Order: $30$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$1254$
Conductor:	$627$
Order:	$30$
Real:	no
Primitive:	no, induced from $\chi_{627}(26,\cdot)$
Minimal:	yes
Parity:	odd

Galois orbit 1254.bi

$\chi_{1254}(125,\cdot)$ $\chi_{1254}(311,\cdot)$ $\chi_{1254}(467,\cdot)$ $\chi_{1254}(581,\cdot)$ $\chi_{1254}(653,\cdot)$ $\chi_{1254}(995,\cdot)$ $\chi_{1254}(1037,\cdot)$ $\chi_{1254}(1109,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{15})$
Fixed field:	Number field defined by a degree 30 polynomial

Values on generators

$(419,343,1123)$ → $(-1,e\left(\frac{1}{5}\right),e\left(\frac{1}{3}\right))$

First values

$a$	$-1$	$1$	$5$	$7$	$13$	$17$	$23$	$25$	$29$	$31$	$35$	$37$
$\chi_{ 1254 }(653, a)$	$-1$	$1$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{19}{30}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{30}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{30}\right)$	$e\left(\frac{2}{5}\right)$