Dirichlet character χ403(202,⋅)\chi_{403}(202,\cdot)

• Label: 403.202
• Modulus: $403$
• Conductor: $403$
• Order: $60$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$403$
Conductor:	$403$
Order:	$60$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 403.ce

$\chi_{403}(2,\cdot)$ $\chi_{403}(33,\cdot)$ $\chi_{403}(97,\cdot)$ $\chi_{403}(128,\cdot)$ $\chi_{403}(132,\cdot)$ $\chi_{403}(163,\cdot)$ $\chi_{403}(171,\cdot)$ $\chi_{403}(188,\cdot)$ $\chi_{403}(202,\cdot)$ $\chi_{403}(219,\cdot)$ $\chi_{403}(314,\cdot)$ $\chi_{403}(318,\cdot)$ $\chi_{403}(345,\cdot)$ $\chi_{403}(349,\cdot)$ $\chi_{403}(357,\cdot)$ $\chi_{403}(388,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{60})$
Fixed field:	Number field defined by a degree 60 polynomial

Values on generators

$(249,313)$ → $(e\left(\frac{11}{12}\right),e\left(\frac{1}{5}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 403 }(202, a)$	$-1$	$1$	$e\left(\frac{43}{60}\right)$	$e\left(\frac{13}{15}\right)$	$e\left(\frac{13}{30}\right)$	$i$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{60}\right)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{11}{15}\right)$	$e\left(\frac{29}{30}\right)$	$e\left(\frac{1}{60}\right)$

Gauss sum

Jacobi sum

Kloosterman sum