Dirichlet character χ1037(710,⋅)\chi_{1037}(710,\cdot)

• Label: 1037.710
• Modulus: $1037$
• Conductor: $1037$
• Order: $60$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1037$
Conductor:	$1037$
Order:	$60$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1037.ch

$\chi_{1037}(4,\cdot)$ $\chi_{1037}(106,\cdot)$ $\chi_{1037}(293,\cdot)$ $\chi_{1037}(310,\cdot)$ $\chi_{1037}(344,\cdot)$ $\chi_{1037}(370,\cdot)$ $\chi_{1037}(412,\cdot)$ $\chi_{1037}(446,\cdot)$ $\chi_{1037}(463,\cdot)$ $\chi_{1037}(472,\cdot)$ $\chi_{1037}(659,\cdot)$ $\chi_{1037}(676,\cdot)$ $\chi_{1037}(710,\cdot)$ $\chi_{1037}(778,\cdot)$ $\chi_{1037}(812,\cdot)$ $\chi_{1037}(829,\cdot)$

Related number fields

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

Values on generators

$(428,307)$ → $(i,e\left(\frac{23}{30}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 1037 }(710, a)$	$1$	$1$	$e\left(\frac{4}{15}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{8}{15}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{7}{60}\right)$	$e\left(\frac{19}{60}\right)$	$e\left(\frac{4}{5}\right)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{23}{60}\right)$	$i$