Dirichlet character χ2299(65,⋅)\chi_{2299}(65,\cdot)

• Label: 2299.65
• Modulus: $2299$
• Conductor: $2299$
• Order: $66$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	$2299$
Conductor:	$2299$
Order:	$66$
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2299.bd

$\chi_{2299}(65,\cdot)$ $\chi_{2299}(164,\cdot)$ $\chi_{2299}(274,\cdot)$ $\chi_{2299}(373,\cdot)$ $\chi_{2299}(582,\cdot)$ $\chi_{2299}(692,\cdot)$ $\chi_{2299}(791,\cdot)$ $\chi_{2299}(901,\cdot)$ $\chi_{2299}(1000,\cdot)$ $\chi_{2299}(1110,\cdot)$ $\chi_{2299}(1319,\cdot)$ $\chi_{2299}(1418,\cdot)$ $\chi_{2299}(1528,\cdot)$ $\chi_{2299}(1627,\cdot)$ $\chi_{2299}(1737,\cdot)$ $\chi_{2299}(1836,\cdot)$ $\chi_{2299}(1946,\cdot)$ $\chi_{2299}(2045,\cdot)$ $\chi_{2299}(2155,\cdot)$ $\chi_{2299}(2254,\cdot)$

Related number fields

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

Values on generators

$(970,1332)$ → $(e\left(\frac{13}{22}\right),e\left(\frac{1}{6}\right))$

First values

$a$	$-1$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$12$
$\chi_{ 2299 }(65, a)$	$1$	$1$	$e\left(\frac{25}{33}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{33}\right)$	$e\left(\frac{13}{33}\right)$	$e\left(\frac{61}{66}\right)$	$e\left(\frac{3}{22}\right)$	$e\left(\frac{3}{11}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{33}\right)$	$e\left(\frac{15}{22}\right)$