Dirichlet character \(\chi_{1309}(37,\cdot)\)

• Label: 1309.37
• 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.db

\(\chi_{1309}(37,\cdot)\) \(\chi_{1309}(58,\cdot)\) \(\chi_{1309}(114,\cdot)\) \(\chi_{1309}(130,\cdot)\) \(\chi_{1309}(158,\cdot)\) \(\chi_{1309}(163,\cdot)\) \(\chi_{1309}(207,\cdot)\) \(\chi_{1309}(214,\cdot)\) \(\chi_{1309}(235,\cdot)\) \(\chi_{1309}(284,\cdot)\) \(\chi_{1309}(312,\cdot)\) \(\chi_{1309}(317,\cdot)\) \(\chi_{1309}(333,\cdot)\) \(\chi_{1309}(345,\cdot)\) \(\chi_{1309}(368,\cdot)\) \(\chi_{1309}(394,\cdot)\) \(\chi_{1309}(401,\cdot)\) \(\chi_{1309}(422,\cdot)\) \(\chi_{1309}(445,\cdot)\) \(\chi_{1309}(466,\cdot)\) \(\chi_{1309}(471,\cdot)\) \(\chi_{1309}(487,\cdot)\) \(\chi_{1309}(499,\cdot)\) \(\chi_{1309}(515,\cdot)\) \(\chi_{1309}(520,\cdot)\) \(\chi_{1309}(522,\cdot)\) \(\chi_{1309}(555,\cdot)\) \(\chi_{1309}(564,\cdot)\) \(\chi_{1309}(592,\cdot)\) \(\chi_{1309}(632,\cdot)\) ...

Related number fields

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

Values on generators

\((1123,596,309)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{5}\right),e\left(\frac{1}{16}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\( \chi_{ 1309 }(37, a) \)	\(-1\)	\(1\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{239}{240}\right)\)	\(e\left(\frac{29}{60}\right)\)	\(e\left(\frac{187}{240}\right)\)	\(e\left(\frac{59}{80}\right)\)	\(e\left(\frac{9}{40}\right)\)	\(e\left(\frac{119}{120}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{9}{20}\right)\)