Dirichlet character \(\chi_{1309}(26,\cdot)\)

• Label: 1309.26
• Modulus: $1309$
• Conductor: $1309$
• Order: $120$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(1309\)
Conductor:	\(1309\)
Order:	\(120\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 1309.cv

\(\chi_{1309}(26,\cdot)\) \(\chi_{1309}(59,\cdot)\) \(\chi_{1309}(185,\cdot)\) \(\chi_{1309}(213,\cdot)\) \(\chi_{1309}(229,\cdot)\) \(\chi_{1309}(236,\cdot)\) \(\chi_{1309}(257,\cdot)\) \(\chi_{1309}(355,\cdot)\) \(\chi_{1309}(383,\cdot)\) \(\chi_{1309}(416,\cdot)\) \(\chi_{1309}(423,\cdot)\) \(\chi_{1309}(444,\cdot)\) \(\chi_{1309}(467,\cdot)\) \(\chi_{1309}(542,\cdot)\) \(\chi_{1309}(570,\cdot)\) \(\chi_{1309}(586,\cdot)\) \(\chi_{1309}(614,\cdot)\) \(\chi_{1309}(621,\cdot)\) \(\chi_{1309}(654,\cdot)\) \(\chi_{1309}(740,\cdot)\) \(\chi_{1309}(773,\cdot)\) \(\chi_{1309}(801,\cdot)\) \(\chi_{1309}(808,\cdot)\) \(\chi_{1309}(852,\cdot)\) \(\chi_{1309}(927,\cdot)\) \(\chi_{1309}(950,\cdot)\) \(\chi_{1309}(971,\cdot)\) \(\chi_{1309}(1039,\cdot)\) \(\chi_{1309}(1137,\cdot)\) \(\chi_{1309}(1158,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{120})$
Fixed field:	Number field defined by a degree 120 polynomial (not computed)

Values on generators

\((1123,596,309)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{5}\right),e\left(\frac{1}{8}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\( \chi_{ 1309 }(26, a) \)	\(-1\)	\(1\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{67}{120}\right)\)	\(e\left(\frac{7}{30}\right)\)	\(e\left(\frac{71}{120}\right)\)	\(e\left(\frac{7}{40}\right)\)	\(e\left(\frac{17}{20}\right)\)	\(e\left(\frac{7}{60}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{1}{5}\right)\)