Dirichlet character \(\chi_{459}(25,\cdot)\)

• Label: 459.25
• Modulus: $459$
• Conductor: $459$
• Order: $72$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 459.ba

\(\chi_{459}(25,\cdot)\) \(\chi_{459}(43,\cdot)\) \(\chi_{459}(49,\cdot)\) \(\chi_{459}(70,\cdot)\) \(\chi_{459}(76,\cdot)\) \(\chi_{459}(94,\cdot)\) \(\chi_{459}(121,\cdot)\) \(\chi_{459}(151,\cdot)\) \(\chi_{459}(178,\cdot)\) \(\chi_{459}(196,\cdot)\) \(\chi_{459}(202,\cdot)\) \(\chi_{459}(223,\cdot)\) \(\chi_{459}(229,\cdot)\) \(\chi_{459}(247,\cdot)\) \(\chi_{459}(274,\cdot)\) \(\chi_{459}(304,\cdot)\) \(\chi_{459}(331,\cdot)\) \(\chi_{459}(349,\cdot)\) \(\chi_{459}(355,\cdot)\) \(\chi_{459}(376,\cdot)\) \(\chi_{459}(382,\cdot)\) \(\chi_{459}(400,\cdot)\) \(\chi_{459}(427,\cdot)\) \(\chi_{459}(457,\cdot)\)

Related number fields

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

Values on generators

\((137,190)\) → \((e\left(\frac{5}{9}\right),e\left(\frac{5}{8}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(4\)	\(5\)	\(7\)	\(8\)	\(10\)	\(11\)	\(13\)	\(14\)	\(16\)
\( \chi_{ 459 }(25, a) \)	\(1\)	\(1\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{2}{9}\right)\)

Gauss sum

Jacobi sum

Kloosterman sum