Dirichlet character χ431(83,⋅)\chi_{431}(83,\cdot)

• Label: 431.83
• Modulus: $431$
• Conductor: $431$
• Order: $430$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$431$
Conductor:	$431$
Order:	$430$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 431.h

$\chi_{431}(7,\cdot)$ $\chi_{431}(13,\cdot)$ $\chi_{431}(14,\cdot)$ $\chi_{431}(17,\cdot)$ $\chi_{431}(21,\cdot)$ $\chi_{431}(28,\cdot)$ $\chi_{431}(31,\cdot)$ $\chi_{431}(34,\cdot)$ $\chi_{431}(35,\cdot)$ $\chi_{431}(37,\cdot)$ $\chi_{431}(39,\cdot)$ $\chi_{431}(42,\cdot)$ $\chi_{431}(43,\cdot)$ $\chi_{431}(51,\cdot)$ $\chi_{431}(52,\cdot)$ $\chi_{431}(56,\cdot)$ $\chi_{431}(62,\cdot)$ $\chi_{431}(63,\cdot)$ $\chi_{431}(65,\cdot)$ $\chi_{431}(67,\cdot)$ $\chi_{431}(68,\cdot)$ $\chi_{431}(70,\cdot)$ $\chi_{431}(71,\cdot)$ $\chi_{431}(73,\cdot)$ $\chi_{431}(74,\cdot)$ $\chi_{431}(77,\cdot)$ $\chi_{431}(78,\cdot)$ $\chi_{431}(79,\cdot)$ $\chi_{431}(83,\cdot)$ $\chi_{431}(84,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{215})$
Fixed field:	Number field defined by a degree 430 polynomial (not computed)

Values on generators

$7$ → $e\left(\frac{323}{430}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 431 }(83, a)$	$-1$	$1$	$e\left(\frac{11}{43}\right)$	$e\left(\frac{14}{43}\right)$	$e\left(\frac{22}{43}\right)$	$e\left(\frac{193}{215}\right)$	$e\left(\frac{25}{43}\right)$	$e\left(\frac{323}{430}\right)$	$e\left(\frac{33}{43}\right)$	$e\left(\frac{28}{43}\right)$	$e\left(\frac{33}{215}\right)$	$e\left(\frac{212}{215}\right)$

Gauss sum

Jacobi sum

Kloosterman sum