Dirichlet character χ1037(190,⋅)\chi_{1037}(190,\cdot)

• Label: 1037.190
• Modulus: $1037$
• Conductor: $1037$
• Order: $240$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$1037$
Conductor:	$1037$
Order:	$240$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1037.cr

$\chi_{1037}(6,\cdot)$ $\chi_{1037}(10,\cdot)$ $\chi_{1037}(63,\cdot)$ $\chi_{1037}(78,\cdot)$ $\chi_{1037}(92,\cdot)$ $\chi_{1037}(96,\cdot)$ $\chi_{1037}(105,\cdot)$ $\chi_{1037}(116,\cdot)$ $\chi_{1037}(124,\cdot)$ $\chi_{1037}(148,\cdot)$ $\chi_{1037}(173,\cdot)$ $\chi_{1037}(176,\cdot)$ $\chi_{1037}(181,\cdot)$ $\chi_{1037}(190,\cdot)$ $\chi_{1037}(193,\cdot)$ $\chi_{1037}(201,\cdot)$ $\chi_{1037}(209,\cdot)$ $\chi_{1037}(214,\cdot)$ $\chi_{1037}(261,\cdot)$ $\chi_{1037}(279,\cdot)$ $\chi_{1037}(335,\cdot)$ $\chi_{1037}(360,\cdot)$ $\chi_{1037}(364,\cdot)$ $\chi_{1037}(396,\cdot)$ $\chi_{1037}(397,\cdot)$ $\chi_{1037}(401,\cdot)$ $\chi_{1037}(445,\cdot)$ $\chi_{1037}(470,\cdot)$ $\chi_{1037}(471,\cdot)$ $\chi_{1037}(486,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{240})$
Fixed field:	Number field defined by a degree 240 polynomial (not computed)

Values on generators

$(428,307)$ → $(e\left(\frac{1}{16}\right),e\left(\frac{49}{60}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 1037 }(190, a)$	$1$	$1$	$e\left(\frac{83}{120}\right)$	$e\left(\frac{77}{80}\right)$	$e\left(\frac{23}{60}\right)$	$e\left(\frac{67}{240}\right)$	$e\left(\frac{157}{240}\right)$	$e\left(\frac{169}{240}\right)$	$e\left(\frac{3}{40}\right)$	$e\left(\frac{37}{40}\right)$	$e\left(\frac{233}{240}\right)$	$e\left(\frac{11}{16}\right)$