Dirichlet character χ862(441,⋅)\chi_{862}(441,\cdot)

• Label: 862.441
• Modulus: $862$
• Conductor: $431$
• Order: $215$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$862$
Conductor:	$431$
Order:	$215$
Real:	no
Primitive:	no, induced from $\chi_{431}(10,\cdot)$
Minimal:	yes
Parity:	even

Galois orbit 862.g

$\chi_{862}(5,\cdot)$ $\chi_{862}(11,\cdot)$ $\chi_{862}(15,\cdot)$ $\chi_{862}(19,\cdot)$ $\chi_{862}(23,\cdot)$ $\chi_{862}(25,\cdot)$ $\chi_{862}(29,\cdot)$ $\chi_{862}(33,\cdot)$ $\chi_{862}(41,\cdot)$ $\chi_{862}(45,\cdot)$ $\chi_{862}(49,\cdot)$ $\chi_{862}(53,\cdot)$ $\chi_{862}(57,\cdot)$ $\chi_{862}(59,\cdot)$ $\chi_{862}(61,\cdot)$ $\chi_{862}(69,\cdot)$ $\chi_{862}(75,\cdot)$ $\chi_{862}(87,\cdot)$ $\chi_{862}(91,\cdot)$ $\chi_{862}(97,\cdot)$ $\chi_{862}(99,\cdot)$ $\chi_{862}(109,\cdot)$ $\chi_{862}(115,\cdot)$ $\chi_{862}(119,\cdot)$ $\chi_{862}(121,\cdot)$ $\chi_{862}(123,\cdot)$ $\chi_{862}(125,\cdot)$ $\chi_{862}(135,\cdot)$ $\chi_{862}(139,\cdot)$ $\chi_{862}(147,\cdot)$ ...

Related number fields

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

Values on generators

$7$ → $e\left(\frac{66}{215}\right)$

First values

$a$	$-1$	$1$	$3$	$5$	$7$	$9$	$11$	$13$	$15$	$17$	$19$	$21$
$\chi_{ 862 }(441, a)$	$1$	$1$	$e\left(\frac{41}{43}\right)$	$e\left(\frac{212}{215}\right)$	$e\left(\frac{66}{215}\right)$	$e\left(\frac{39}{43}\right)$	$e\left(\frac{68}{215}\right)$	$e\left(\frac{57}{215}\right)$	$e\left(\frac{202}{215}\right)$	$e\left(\frac{111}{215}\right)$	$e\left(\frac{89}{215}\right)$	$e\left(\frac{56}{215}\right)$

Gauss sum

Jacobi sum

Kloosterman sum