Dirichlet character χ229(30,⋅)\chi_{229}(30,\cdot)

• Label: 229.30
• Modulus: $229$
• Conductor: $229$
• Order: $76$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$229$
Conductor:	$229$
Order:	$76$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 229.j

$\chi_{229}(2,\cdot)$ $\chi_{229}(8,\cdot)$ $\chi_{229}(13,\cdot)$ $\chi_{229}(21,\cdot)$ $\chi_{229}(22,\cdot)$ $\chi_{229}(30,\cdot)$ $\chi_{229}(32,\cdot)$ $\chi_{229}(34,\cdot)$ $\chi_{229}(52,\cdot)$ $\chi_{229}(54,\cdot)$ $\chi_{229}(84,\cdot)$ $\chi_{229}(86,\cdot)$ $\chi_{229}(88,\cdot)$ $\chi_{229}(93,\cdot)$ $\chi_{229}(101,\cdot)$ $\chi_{229}(106,\cdot)$ $\chi_{229}(109,\cdot)$ $\chi_{229}(114,\cdot)$ $\chi_{229}(115,\cdot)$ $\chi_{229}(120,\cdot)$ $\chi_{229}(123,\cdot)$ $\chi_{229}(128,\cdot)$ $\chi_{229}(136,\cdot)$ $\chi_{229}(141,\cdot)$ $\chi_{229}(143,\cdot)$ $\chi_{229}(145,\cdot)$ $\chi_{229}(175,\cdot)$ $\chi_{229}(177,\cdot)$ $\chi_{229}(195,\cdot)$ $\chi_{229}(197,\cdot)$ ...

Related number fields

Field of values:	$\Q(\zeta_{76})$
Fixed field:	Number field defined by a degree 76 polynomial

Values on generators

$6$ → $e\left(\frac{33}{76}\right)$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$\chi_{ 229 }(30, a)$	$-1$	$1$	$e\left(\frac{9}{76}\right)$	$e\left(\frac{6}{19}\right)$	$e\left(\frac{9}{38}\right)$	$e\left(\frac{21}{38}\right)$	$e\left(\frac{33}{76}\right)$	$e\left(\frac{35}{76}\right)$	$e\left(\frac{27}{76}\right)$	$e\left(\frac{12}{19}\right)$	$e\left(\frac{51}{76}\right)$	$e\left(\frac{13}{38}\right)$

Gauss sum

Jacobi sum

Kloosterman sum