Dirichlet character χ841(33,⋅)\chi_{841}(33,\cdot)

• Label: 841.33
• Modulus: $841$
• Conductor: $841$
• Order: $406$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$841$
Conductor:	$841$
Order:	$406$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 841.k

$\chi_{841}(4,\cdot)$ $\chi_{841}(5,\cdot)$ $\chi_{841}(6,\cdot)$ $\chi_{841}(9,\cdot)$ $\chi_{841}(13,\cdot)$ $\chi_{841}(22,\cdot)$ $\chi_{841}(33,\cdot)$ $\chi_{841}(34,\cdot)$ $\chi_{841}(35,\cdot)$ $\chi_{841}(38,\cdot)$ $\chi_{841}(42,\cdot)$ $\chi_{841}(51,\cdot)$ $\chi_{841}(62,\cdot)$ $\chi_{841}(64,\cdot)$ $\chi_{841}(67,\cdot)$ $\chi_{841}(71,\cdot)$ $\chi_{841}(80,\cdot)$ $\chi_{841}(91,\cdot)$ $\chi_{841}(92,\cdot)$ $\chi_{841}(93,\cdot)$ $\chi_{841}(96,\cdot)$ $\chi_{841}(100,\cdot)$ $\chi_{841}(109,\cdot)$ $\chi_{841}(120,\cdot)$ $\chi_{841}(121,\cdot)$ $\chi_{841}(122,\cdot)$ $\chi_{841}(125,\cdot)$ $\chi_{841}(129,\cdot)$ $\chi_{841}(138,\cdot)$ $\chi_{841}(149,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{203})$
Fixed field:	Number field defined by a degree 406 polynomial (not computed)

Values on generators

$2$ → $e\left(\frac{309}{406}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 841 }(33, a)$	$1$	$1$	$e\left(\frac{309}{406}\right)$	$e\left(\frac{285}{406}\right)$	$e\left(\frac{106}{203}\right)$	$e\left(\frac{172}{203}\right)$	$e\left(\frac{94}{203}\right)$	$e\left(\frac{34}{203}\right)$	$e\left(\frac{115}{406}\right)$	$e\left(\frac{82}{203}\right)$	$e\left(\frac{247}{406}\right)$	$e\left(\frac{263}{406}\right)$

Gauss sum

Jacobi sum

Kloosterman sum