Dirichlet character χ100315(753,⋅)\chi_{100315}(753,\cdot)

• Label: 100315.753
• Modulus: $100315$
• Conductor: $100315$
• Order: $5732$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$100315$
Conductor:	$100315$
Order:	$5732$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 100315.r

$\chi_{100315}(2,\cdot)$ $\chi_{100315}(8,\cdot)$ $\chi_{100315}(32,\cdot)$ $\chi_{100315}(47,\cdot)$ $\chi_{100315}(73,\cdot)$ $\chi_{100315}(87,\cdot)$ $\chi_{100315}(128,\cdot)$ $\chi_{100315}(137,\cdot)$ $\chi_{100315}(188,\cdot)$ $\chi_{100315}(223,\cdot)$ $\chi_{100315}(292,\cdot)$ $\chi_{100315}(317,\cdot)$ $\chi_{100315}(348,\cdot)$ $\chi_{100315}(357,\cdot)$ $\chi_{100315}(363,\cdot)$ $\chi_{100315}(377,\cdot)$ $\chi_{100315}(398,\cdot)$ $\chi_{100315}(422,\cdot)$ $\chi_{100315}(512,\cdot)$ $\chi_{100315}(548,\cdot)$ $\chi_{100315}(562,\cdot)$ $\chi_{100315}(613,\cdot)$ $\chi_{100315}(627,\cdot)$ $\chi_{100315}(697,\cdot)$ $\chi_{100315}(752,\cdot)$ $\chi_{100315}(753,\cdot)$ $\chi_{100315}(877,\cdot)$ $\chi_{100315}(892,\cdot)$ $\chi_{100315}(913,\cdot)$ $\chi_{100315}(917,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{5732})$
Fixed field:	Number field defined by a degree 5732 polynomial (not computed)

Values on generators

$(40127,40131)$ → $(-i,e\left(\frac{11}{1433}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 100315 }(753, a)$	$-1$	$1$	$e\left(\frac{1723}{5732}\right)$	$e\left(\frac{5321}{5732}\right)$	$e\left(\frac{1723}{2866}\right)$	$e\left(\frac{328}{1433}\right)$	$e\left(\frac{1015}{5732}\right)$	$e\left(\frac{5169}{5732}\right)$	$e\left(\frac{2455}{2866}\right)$	$e\left(\frac{821}{1433}\right)$	$e\left(\frac{3035}{5732}\right)$	$e\left(\frac{3553}{5732}\right)$