Dirichlet character \(\chi_{483}(4,\cdot)\)

• Label: 483.4
• Modulus: $483$
• Conductor: $161$
• Order: $33$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(483\)
Conductor:	\(161\)
Order:	\(33\)
Real:	no
Primitive:	no, induced from \(\chi_{161}(4,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 483.y

\(\chi_{483}(4,\cdot)\) \(\chi_{483}(16,\cdot)\) \(\chi_{483}(25,\cdot)\) \(\chi_{483}(58,\cdot)\) \(\chi_{483}(100,\cdot)\) \(\chi_{483}(121,\cdot)\) \(\chi_{483}(142,\cdot)\) \(\chi_{483}(151,\cdot)\) \(\chi_{483}(163,\cdot)\) \(\chi_{483}(193,\cdot)\) \(\chi_{483}(256,\cdot)\) \(\chi_{483}(289,\cdot)\) \(\chi_{483}(331,\cdot)\) \(\chi_{483}(340,\cdot)\) \(\chi_{483}(361,\cdot)\) \(\chi_{483}(394,\cdot)\) \(\chi_{483}(403,\cdot)\) \(\chi_{483}(445,\cdot)\) \(\chi_{483}(466,\cdot)\) \(\chi_{483}(478,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{33})\)
Fixed field:	33.33.277966181338944111003326058293667039541136678070715028736001.1

Values on generators

\((323,346,442)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{2}{11}\right))\)

Values

\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(8\)	\(10\)	\(11\)	\(13\)	\(16\)	\(17\)	\(19\)
\(1\)	\(1\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{1}{11}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)	\(e\left(\frac{26}{33}\right)\)	\(e\left(\frac{31}{33}\right)\)	\(e\left(\frac{2}{33}\right)\)

value at

e.g. 2

Gauss sum

\(\displaystyle \tau_{2}(\chi_{483}(4,\cdot)) = \sum_{r\in \Z/483\Z} \chi_{483}(4,r) e\left(\frac{2r}{483}\right) = -5.8904074034+11.2384652254i \)

Jacobi sum

\( \displaystyle J(\chi_{483}(4,\cdot),\chi_{483}(1,\cdot)) = \sum_{r\in \Z/483\Z} \chi_{483}(4,r) \chi_{483}(1,1-r) = 1 \)

Kloosterman sum

\( \displaystyle K(1,2,\chi_{483}(4,·)) = \sum_{r \in \Z/483\Z} \chi_{483}(4,r) e\left(\frac{1 r + 2 r^{-1}}{483}\right) = 7.3496719946+-10.3211701533i \)