Dirichlet character \(\chi_{1309}(25,\cdot)\)

• Label: 1309.25
• Modulus: $1309$
• Conductor: $1309$
• Order: $120$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

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

Galois orbit 1309.cx

\(\chi_{1309}(9,\cdot)\) \(\chi_{1309}(25,\cdot)\) \(\chi_{1309}(53,\cdot)\) \(\chi_{1309}(60,\cdot)\) \(\chi_{1309}(93,\cdot)\) \(\chi_{1309}(179,\cdot)\) \(\chi_{1309}(212,\cdot)\) \(\chi_{1309}(240,\cdot)\) \(\chi_{1309}(247,\cdot)\) \(\chi_{1309}(291,\cdot)\) \(\chi_{1309}(366,\cdot)\) \(\chi_{1309}(389,\cdot)\) \(\chi_{1309}(410,\cdot)\) \(\chi_{1309}(478,\cdot)\) \(\chi_{1309}(576,\cdot)\) \(\chi_{1309}(597,\cdot)\) \(\chi_{1309}(620,\cdot)\) \(\chi_{1309}(746,\cdot)\) \(\chi_{1309}(774,\cdot)\) \(\chi_{1309}(807,\cdot)\) \(\chi_{1309}(933,\cdot)\) \(\chi_{1309}(961,\cdot)\) \(\chi_{1309}(977,\cdot)\) \(\chi_{1309}(984,\cdot)\) \(\chi_{1309}(1005,\cdot)\) \(\chi_{1309}(1103,\cdot)\) \(\chi_{1309}(1131,\cdot)\) \(\chi_{1309}(1164,\cdot)\) \(\chi_{1309}(1171,\cdot)\) \(\chi_{1309}(1192,\cdot)\) ...

Related number fields

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

Values on generators

\((1123,596,309)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{4}{5}\right),e\left(\frac{5}{8}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\( \chi_{ 1309 }(25, a) \)	\(1\)	\(1\)	\(e\left(\frac{53}{60}\right)\)	\(e\left(\frac{83}{120}\right)\)	\(e\left(\frac{23}{30}\right)\)	\(e\left(\frac{79}{120}\right)\)	\(e\left(\frac{23}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{23}{60}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{3}{10}\right)\)