Dirichlet character \(\chi_{1309}(19,\cdot)\)

• Label: 1309.19
• 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.cw

\(\chi_{1309}(19,\cdot)\) \(\chi_{1309}(94,\cdot)\) \(\chi_{1309}(117,\cdot)\) \(\chi_{1309}(138,\cdot)\) \(\chi_{1309}(145,\cdot)\) \(\chi_{1309}(178,\cdot)\) \(\chi_{1309}(206,\cdot)\) \(\chi_{1309}(304,\cdot)\) \(\chi_{1309}(325,\cdot)\) \(\chi_{1309}(332,\cdot)\) \(\chi_{1309}(348,\cdot)\) \(\chi_{1309}(376,\cdot)\) \(\chi_{1309}(502,\cdot)\) \(\chi_{1309}(535,\cdot)\) \(\chi_{1309}(563,\cdot)\) \(\chi_{1309}(689,\cdot)\) \(\chi_{1309}(712,\cdot)\) \(\chi_{1309}(733,\cdot)\) \(\chi_{1309}(831,\cdot)\) \(\chi_{1309}(899,\cdot)\) \(\chi_{1309}(920,\cdot)\) \(\chi_{1309}(943,\cdot)\) \(\chi_{1309}(1018,\cdot)\) \(\chi_{1309}(1062,\cdot)\) \(\chi_{1309}(1069,\cdot)\) \(\chi_{1309}(1097,\cdot)\) \(\chi_{1309}(1130,\cdot)\) \(\chi_{1309}(1216,\cdot)\) \(\chi_{1309}(1249,\cdot)\) \(\chi_{1309}(1256,\cdot)\) ...

Related number fields

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

Values on generators

\((1123,596,309)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{3}{10}\right),e\left(\frac{7}{8}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\( \chi_{ 1309 }(19, a) \)	\(1\)	\(1\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{13}{120}\right)\)	\(e\left(\frac{13}{30}\right)\)	\(e\left(\frac{89}{120}\right)\)	\(e\left(\frac{13}{40}\right)\)	\(e\left(\frac{13}{20}\right)\)	\(e\left(\frac{13}{60}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{3}{10}\right)\)