Dirichlet character \(\chi_{459}(2,\cdot)\)

• Label: 459.2
• Modulus: $459$
• Conductor: $459$
• Order: $72$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(459\)
Conductor:	\(459\)
Order:	\(72\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 459.bb

\(\chi_{459}(2,\cdot)\) \(\chi_{459}(32,\cdot)\) \(\chi_{459}(59,\cdot)\) \(\chi_{459}(77,\cdot)\) \(\chi_{459}(83,\cdot)\) \(\chi_{459}(104,\cdot)\) \(\chi_{459}(110,\cdot)\) \(\chi_{459}(128,\cdot)\) \(\chi_{459}(155,\cdot)\) \(\chi_{459}(185,\cdot)\) \(\chi_{459}(212,\cdot)\) \(\chi_{459}(230,\cdot)\) \(\chi_{459}(236,\cdot)\) \(\chi_{459}(257,\cdot)\) \(\chi_{459}(263,\cdot)\) \(\chi_{459}(281,\cdot)\) \(\chi_{459}(308,\cdot)\) \(\chi_{459}(338,\cdot)\) \(\chi_{459}(365,\cdot)\) \(\chi_{459}(383,\cdot)\) \(\chi_{459}(389,\cdot)\) \(\chi_{459}(410,\cdot)\) \(\chi_{459}(416,\cdot)\) \(\chi_{459}(434,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{72})$
Fixed field:	Number field defined by a degree 72 polynomial

Values on generators

\((137,190)\) → \((e\left(\frac{1}{18}\right),e\left(\frac{7}{8}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 459 }(2, a) \)	\(-1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum