Dirichlet character χ1037(143,⋅)\chi_{1037}(143,\cdot)

• Label: 1037.143
• Modulus: $1037$
• Conductor: $1037$
• Order: $48$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1037$
Conductor:	$1037$
Order:	$48$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1037.bz

$\chi_{1037}(143,\cdot)$ $\chi_{1037}(265,\cdot)$ $\chi_{1037}(284,\cdot)$ $\chi_{1037}(334,\cdot)$ $\chi_{1037}(337,\cdot)$ $\chi_{1037}(345,\cdot)$ $\chi_{1037}(448,\cdot)$ $\chi_{1037}(517,\cdot)$ $\chi_{1037}(581,\cdot)$ $\chi_{1037}(639,\cdot)$ $\chi_{1037}(711,\cdot)$ $\chi_{1037}(822,\cdot)$ $\chi_{1037}(947,\cdot)$ $\chi_{1037}(955,\cdot)$ $\chi_{1037}(997,\cdot)$ $\chi_{1037}(1008,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{48})$
Fixed field:	Number field defined by a degree 48 polynomial

Values on generators

$(428,307)$ → $(e\left(\frac{11}{16}\right),e\left(\frac{11}{12}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 1037 }(143, a)$	$1$	$1$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{3}{16}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{9}{16}\right)$