Dirichlet character χ95(78,⋅)\chi_{95}(78,\cdot)

• Label: 95.78
• Modulus: $95$
• Conductor: $95$
• Order: $36$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$95$
Conductor:	$95$
Order:	$36$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 95.r

$\chi_{95}(2,\cdot)$ $\chi_{95}(3,\cdot)$ $\chi_{95}(13,\cdot)$ $\chi_{95}(22,\cdot)$ $\chi_{95}(32,\cdot)$ $\chi_{95}(33,\cdot)$ $\chi_{95}(48,\cdot)$ $\chi_{95}(52,\cdot)$ $\chi_{95}(53,\cdot)$ $\chi_{95}(67,\cdot)$ $\chi_{95}(72,\cdot)$ $\chi_{95}(78,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{36})$
Fixed field:	$\Q(\zeta_{95})^+$

Values on generators

$(77,21)$ → $(-i,e\left(\frac{1}{18}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$6$	$7$	$8$	$9$	$11$	$12$	$13$
$\chi_{ 95 }(78, a)$	$1$	$1$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{19}{36}\right)$

Gauss sum

Jacobi sum

Kloosterman sum