Dirichlet character χ1037(516,⋅)\chi_{1037}(516,\cdot)

• Label: 1037.516
• Modulus: $1037$
• Conductor: $1037$
• Order: $80$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1037$
Conductor:	$1037$
Order:	$80$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1037.ck

$\chi_{1037}(28,\cdot)$ $\chi_{1037}(114,\cdot)$ $\chi_{1037}(130,\cdot)$ $\chi_{1037}(159,\cdot)$ $\chi_{1037}(160,\cdot)$ $\chi_{1037}(175,\cdot)$ $\chi_{1037}(207,\cdot)$ $\chi_{1037}(211,\cdot)$ $\chi_{1037}(216,\cdot)$ $\chi_{1037}(267,\cdot)$ $\chi_{1037}(277,\cdot)$ $\chi_{1037}(282,\cdot)$ $\chi_{1037}(313,\cdot)$ $\chi_{1037}(328,\cdot)$ $\chi_{1037}(333,\cdot)$ $\chi_{1037}(435,\cdot)$ $\chi_{1037}(465,\cdot)$ $\chi_{1037}(516,\cdot)$ $\chi_{1037}(541,\cdot)$ $\chi_{1037}(573,\cdot)$ $\chi_{1037}(618,\cdot)$ $\chi_{1037}(634,\cdot)$ $\chi_{1037}(643,\cdot)$ $\chi_{1037}(694,\cdot)$ $\chi_{1037}(708,\cdot)$ $\chi_{1037}(785,\cdot)$ $\chi_{1037}(887,\cdot)$ $\chi_{1037}(891,\cdot)$ $\chi_{1037}(938,\cdot)$ $\chi_{1037}(1000,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{80})$
Fixed field:	Number field defined by a degree 80 polynomial

Values on generators

$(428,307)$ → $(e\left(\frac{15}{16}\right),e\left(\frac{17}{20}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 1037 }(516, a)$	$1$	$1$	$e\left(\frac{39}{40}\right)$	$e\left(\frac{3}{80}\right)$	$e\left(\frac{19}{20}\right)$	$e\left(\frac{31}{80}\right)$	$e\left(\frac{1}{80}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{29}{80}\right)$	$e\left(\frac{5}{16}\right)$