Dirichlet character \(\chi_{1309}(24,\cdot)\)

• Label: 1309.24
• Modulus: $1309$
• Conductor: $1309$
• Order: $240$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1309\)
Conductor:	\(1309\)
Order:	\(240\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1309.cz

\(\chi_{1309}(24,\cdot)\) \(\chi_{1309}(40,\cdot)\) \(\chi_{1309}(61,\cdot)\) \(\chi_{1309}(73,\cdot)\) \(\chi_{1309}(96,\cdot)\) \(\chi_{1309}(129,\cdot)\) \(\chi_{1309}(150,\cdot)\) \(\chi_{1309}(173,\cdot)\) \(\chi_{1309}(194,\cdot)\) \(\chi_{1309}(215,\cdot)\) \(\chi_{1309}(227,\cdot)\) \(\chi_{1309}(248,\cdot)\) \(\chi_{1309}(250,\cdot)\) \(\chi_{1309}(283,\cdot)\) \(\chi_{1309}(292,\cdot)\) \(\chi_{1309}(299,\cdot)\) \(\chi_{1309}(360,\cdot)\) \(\chi_{1309}(369,\cdot)\) \(\chi_{1309}(381,\cdot)\) \(\chi_{1309}(402,\cdot)\) \(\chi_{1309}(437,\cdot)\) \(\chi_{1309}(453,\cdot)\) \(\chi_{1309}(479,\cdot)\) \(\chi_{1309}(481,\cdot)\) \(\chi_{1309}(486,\cdot)\) \(\chi_{1309}(530,\cdot)\) \(\chi_{1309}(556,\cdot)\) \(\chi_{1309}(558,\cdot)\) \(\chi_{1309}(600,\cdot)\) \(\chi_{1309}(607,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{240})$
Fixed field:	Number field defined by a degree 240 polynomial (not computed)

Values on generators

\((1123,596,309)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{1}{10}\right),e\left(\frac{11}{16}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\( \chi_{ 1309 }(24, a) \)	\(-1\)	\(1\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{157}{240}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{161}{240}\right)\)	\(e\left(\frac{57}{80}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{37}{120}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{20}\right)\)