Dirichlet character χ1037(110,⋅)\chi_{1037}(110,\cdot)

• Label: 1037.110
• Modulus: $1037$
• Conductor: $1037$
• Order: $120$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1037$
Conductor:	$1037$
Order:	$120$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1037.cn

$\chi_{1037}(19,\cdot)$ $\chi_{1037}(36,\cdot)$ $\chi_{1037}(49,\cdot)$ $\chi_{1037}(66,\cdot)$ $\chi_{1037}(100,\cdot)$ $\chi_{1037}(110,\cdot)$ $\chi_{1037}(127,\cdot)$ $\chi_{1037}(161,\cdot)$ $\chi_{1037}(168,\cdot)$ $\chi_{1037}(202,\cdot)$ $\chi_{1037}(219,\cdot)$ $\chi_{1037}(229,\cdot)$ $\chi_{1037}(263,\cdot)$ $\chi_{1037}(280,\cdot)$ $\chi_{1037}(553,\cdot)$ $\chi_{1037}(614,\cdot)$ $\chi_{1037}(655,\cdot)$ $\chi_{1037}(716,\cdot)$ $\chi_{1037}(797,\cdot)$ $\chi_{1037}(842,\cdot)$ $\chi_{1037}(858,\cdot)$ $\chi_{1037}(859,\cdot)$ $\chi_{1037}(893,\cdot)$ $\chi_{1037}(899,\cdot)$ $\chi_{1037}(903,\cdot)$ $\chi_{1037}(920,\cdot)$ $\chi_{1037}(954,\cdot)$ $\chi_{1037}(960,\cdot)$ $\chi_{1037}(961,\cdot)$ $\chi_{1037}(995,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{120})$
Fixed field:	Number field defined by a degree 120 polynomial (not computed)

Values on generators

$(428,307)$ → $(e\left(\frac{5}{8}\right),e\left(\frac{19}{30}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 1037 }(110, a)$	$1$	$1$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{17}{40}\right)$	$e\left(\frac{23}{30}\right)$	$e\left(\frac{7}{120}\right)$	$e\left(\frac{97}{120}\right)$	$e\left(\frac{109}{120}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{53}{120}\right)$	$e\left(\frac{7}{8}\right)$