Dirichlet character \(\chi_{547}(296,\cdot)\)

• Label: 547.296
• Modulus: $547$
• Conductor: $547$
• Order: $39$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(547\)
Conductor:	\(547\)
Order:	\(39\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 547.j

\(\chi_{547}(11,\cdot)\) \(\chi_{547}(21,\cdot)\) \(\chi_{547}(47,\cdot)\) \(\chi_{547}(54,\cdot)\) \(\chi_{547}(96,\cdot)\) \(\chi_{547}(121,\cdot)\) \(\chi_{547}(129,\cdot)\) \(\chi_{547}(136,\cdot)\) \(\chi_{547}(181,\cdot)\) \(\chi_{547}(199,\cdot)\) \(\chi_{547}(217,\cdot)\) \(\chi_{547}(231,\cdot)\) \(\chi_{547}(233,\cdot)\) \(\chi_{547}(239,\cdot)\) \(\chi_{547}(296,\cdot)\) \(\chi_{547}(302,\cdot)\) \(\chi_{547}(325,\cdot)\) \(\chi_{547}(402,\cdot)\) \(\chi_{547}(419,\cdot)\) \(\chi_{547}(441,\cdot)\) \(\chi_{547}(445,\cdot)\) \(\chi_{547}(464,\cdot)\) \(\chi_{547}(488,\cdot)\) \(\chi_{547}(521,\cdot)\)

Values on generators

\(2\) → \(e\left(\frac{35}{39}\right)\)

Values

\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\(1\)	\(1\)	\(e\left(\frac{35}{39}\right)\)	\(1\)	\(e\left(\frac{31}{39}\right)\)	\(e\left(\frac{25}{39}\right)\)	\(e\left(\frac{35}{39}\right)\)	\(e\left(\frac{17}{39}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(1\)	\(e\left(\frac{7}{13}\right)\)	\(e\left(\frac{32}{39}\right)\)

value at

e.g. 2

Related number fields

Field of values:	$\Q(\zeta_{39})$
Fixed field:	39.39.110539730308983252644692019573737637228828219789892386533857010792412648335681998371651796263456819412889.1

Gauss sum

\(\displaystyle \tau_{2}(\chi_{547}(296,\cdot)) = \sum_{r\in \Z/547\Z} \chi_{547}(296,r) e\left(\frac{2r}{547}\right) = -6.2267772402+-22.5438959632i \)

Jacobi sum

\( \displaystyle J(\chi_{547}(296,\cdot),\chi_{547}(1,\cdot)) = \sum_{r\in \Z/547\Z} \chi_{547}(296,r) \chi_{547}(1,1-r) = -1 \)

Kloosterman sum

\( \displaystyle K(1,2,\chi_{547}(296,·)) = \sum_{r \in \Z/547\Z} \chi_{547}(296,r) e\left(\frac{1 r + 2 r^{-1}}{547}\right) = -8.4341323458+2.8157271047i \)