Dirichlet character χ735(29,⋅)\chi_{735}(29,\cdot)

• Label: 735.29
• Modulus: $735$
• Conductor: $735$
• Order: $14$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$735$
Conductor:	$735$
Order:	$14$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 735.bb

$\chi_{735}(29,\cdot)$ $\chi_{735}(134,\cdot)$ $\chi_{735}(239,\cdot)$ $\chi_{735}(449,\cdot)$ $\chi_{735}(554,\cdot)$ $\chi_{735}(659,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{7})$
Fixed field:	Number field defined by a degree 14 polynomial

Values on generators

$(491,442,346)$ → $(-1,-1,e\left(\frac{3}{7}\right))$

First values

$a$	$-1$	$1$	$2$	$4$	$8$	$11$	$13$	$16$	$17$	$19$	$22$	$23$
$\chi_{ 735 }(29, a)$	$-1$	$1$	$e\left(\frac{1}{7}\right)$	$e\left(\frac{2}{7}\right)$	$e\left(\frac{3}{7}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{9}{14}\right)$	$e\left(\frac{4}{7}\right)$	$e\left(\frac{5}{7}\right)$	$1$	$e\left(\frac{11}{14}\right)$	$e\left(\frac{2}{7}\right)$

Gauss sum

Jacobi sum

Kloosterman sum