Dirichlet character χ161(149,⋅)\chi_{161}(149,\cdot)

• Label: 161.149
• Modulus: $161$
• Conductor: $161$
• Order: $66$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	$161$
Conductor:	$161$
Order:	$66$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 161.p

$\chi_{161}(11,\cdot)$ $\chi_{161}(30,\cdot)$ $\chi_{161}(37,\cdot)$ $\chi_{161}(44,\cdot)$ $\chi_{161}(51,\cdot)$ $\chi_{161}(53,\cdot)$ $\chi_{161}(60,\cdot)$ $\chi_{161}(65,\cdot)$ $\chi_{161}(67,\cdot)$ $\chi_{161}(74,\cdot)$ $\chi_{161}(79,\cdot)$ $\chi_{161}(86,\cdot)$ $\chi_{161}(88,\cdot)$ $\chi_{161}(102,\cdot)$ $\chi_{161}(107,\cdot)$ $\chi_{161}(109,\cdot)$ $\chi_{161}(130,\cdot)$ $\chi_{161}(135,\cdot)$ $\chi_{161}(149,\cdot)$ $\chi_{161}(158,\cdot)$

Related number fields

Field of values:	$\Q(\zeta_{33})$
Fixed field:	Number field defined by a degree 66 polynomial

Values on generators

$(24,120)$ → $(e\left(\frac{1}{3}\right),e\left(\frac{9}{22}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$	$12$
$\chi_{ 161 }(149, a)$	$-1$	$1$	$e\left(\frac{16}{33}\right)$	$e\left(\frac{29}{33}\right)$	$e\left(\frac{32}{33}\right)$	$e\left(\frac{5}{66}\right)$	$e\left(\frac{4}{11}\right)$	$e\left(\frac{5}{11}\right)$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{37}{66}\right)$	$e\left(\frac{1}{66}\right)$	$e\left(\frac{28}{33}\right)$

Gauss sum

Jacobi sum

Kloosterman sum