Dirichlet character χ119(97,⋅)\chi_{119}(97,\cdot)

• Label: 119.97
• Modulus: $119$
• Conductor: $119$
• Order: $16$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$119$
Conductor:	$119$
Order:	$16$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 119.p

$\chi_{119}(6,\cdot)$ $\chi_{119}(20,\cdot)$ $\chi_{119}(27,\cdot)$ $\chi_{119}(41,\cdot)$ $\chi_{119}(48,\cdot)$ $\chi_{119}(62,\cdot)$ $\chi_{119}(90,\cdot)$ $\chi_{119}(97,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{16})$
Fixed field:	16.16.16501299269766837593302193.1

Values on generators

$(52,71)$ → $(-1,e\left(\frac{13}{16}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{ 119 }(97, a)$	$1$	$1$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{5}{16}\right)$	$-i$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{15}{16}\right)$	$e\left(\frac{11}{16}\right)$	$e\left(\frac{1}{16}\right)$

Gauss sum

Jacobi sum

Kloosterman sum