Dirichlet character \(\chi_{1309}(1124,\cdot)\)

• Label: 1309.1124
• 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.cu

\(\chi_{1309}(2,\cdot)\) \(\chi_{1309}(128,\cdot)\) \(\chi_{1309}(151,\cdot)\) \(\chi_{1309}(172,\cdot)\) \(\chi_{1309}(270,\cdot)\) \(\chi_{1309}(338,\cdot)\) \(\chi_{1309}(359,\cdot)\) \(\chi_{1309}(382,\cdot)\) \(\chi_{1309}(457,\cdot)\) \(\chi_{1309}(501,\cdot)\) \(\chi_{1309}(508,\cdot)\) \(\chi_{1309}(536,\cdot)\) \(\chi_{1309}(569,\cdot)\) \(\chi_{1309}(655,\cdot)\) \(\chi_{1309}(688,\cdot)\) \(\chi_{1309}(695,\cdot)\) \(\chi_{1309}(723,\cdot)\) \(\chi_{1309}(739,\cdot)\) \(\chi_{1309}(767,\cdot)\) \(\chi_{1309}(842,\cdot)\) \(\chi_{1309}(865,\cdot)\) \(\chi_{1309}(886,\cdot)\) \(\chi_{1309}(893,\cdot)\) \(\chi_{1309}(926,\cdot)\) \(\chi_{1309}(954,\cdot)\) \(\chi_{1309}(1052,\cdot)\) \(\chi_{1309}(1073,\cdot)\) \(\chi_{1309}(1080,\cdot)\) \(\chi_{1309}(1096,\cdot)\) \(\chi_{1309}(1124,\cdot)\) ...

Related number fields

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

Values on generators

\((1123,596,309)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{1}{10}\right),e\left(\frac{7}{8}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\( \chi_{ 1309 }(1124, a) \)	\(-1\)	\(1\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{41}{120}\right)\)	\(e\left(\frac{11}{30}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{1}{40}\right)\)	\(e\left(\frac{1}{20}\right)\)	\(e\left(\frac{41}{60}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{3}{5}\right)\)