Dirichlet character \(\chi_{469}(282,\cdot)\)

• Label: 469.282
• Modulus: $469$
• Conductor: $469$
• Order: $33$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(469\)
Conductor:	\(469\)
Order:	\(33\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 469.ba

\(\chi_{469}(9,\cdot)\) \(\chi_{469}(25,\cdot)\) \(\chi_{469}(81,\cdot)\) \(\chi_{469}(107,\cdot)\) \(\chi_{469}(149,\cdot)\) \(\chi_{469}(156,\cdot)\) \(\chi_{469}(158,\cdot)\) \(\chi_{469}(193,\cdot)\) \(\chi_{469}(198,\cdot)\) \(\chi_{469}(226,\cdot)\) \(\chi_{469}(263,\cdot)\) \(\chi_{469}(277,\cdot)\) \(\chi_{469}(282,\cdot)\) \(\chi_{469}(359,\cdot)\) \(\chi_{469}(375,\cdot)\) \(\chi_{469}(394,\cdot)\) \(\chi_{469}(417,\cdot)\) \(\chi_{469}(424,\cdot)\) \(\chi_{469}(464,\cdot)\) \(\chi_{469}(466,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{33})\)
Fixed field:	33.33.23681050358190252966666038984115482490423545779778728084912954382239302601.1

Values on generators

\((269,337)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{4}{11}\right))\)

Values

\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(11\)	\(12\)
\(1\)	\(1\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{4}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{5}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{19}{33}\right)\)

value at

e.g. 2

Gauss sum

\(\displaystyle \tau_{2}(\chi_{469}(282,\cdot)) = \sum_{r\in \Z/469\Z} \chi_{469}(282,r) e\left(\frac{2r}{469}\right) = 20.3062193651+7.5271146595i \)

Jacobi sum

\( \displaystyle J(\chi_{469}(282,\cdot),\chi_{469}(1,\cdot)) = \sum_{r\in \Z/469\Z} \chi_{469}(282,r) \chi_{469}(1,1-r) = 1 \)

Kloosterman sum

\( \displaystyle K(1,2,\chi_{469}(282,·)) = \sum_{r \in \Z/469\Z} \chi_{469}(282,r) e\left(\frac{1 r + 2 r^{-1}}{469}\right) = 25.422316378+2.4275368815i \)