Dirichlet character \(\chi_{1309}(31,\cdot)\)

• Label: 1309.31
• Modulus: $1309$
• Conductor: $1309$
• Order: $240$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(1309\)
Conductor:	\(1309\)
Order:	\(240\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 1309.da

\(\chi_{1309}(3,\cdot)\) \(\chi_{1309}(5,\cdot)\) \(\chi_{1309}(31,\cdot)\) \(\chi_{1309}(75,\cdot)\) \(\chi_{1309}(80,\cdot)\) \(\chi_{1309}(82,\cdot)\) \(\chi_{1309}(108,\cdot)\) \(\chi_{1309}(124,\cdot)\) \(\chi_{1309}(159,\cdot)\) \(\chi_{1309}(180,\cdot)\) \(\chi_{1309}(192,\cdot)\) \(\chi_{1309}(201,\cdot)\) \(\chi_{1309}(262,\cdot)\) \(\chi_{1309}(269,\cdot)\) \(\chi_{1309}(278,\cdot)\) \(\chi_{1309}(311,\cdot)\) \(\chi_{1309}(313,\cdot)\) \(\chi_{1309}(334,\cdot)\) \(\chi_{1309}(346,\cdot)\) \(\chi_{1309}(367,\cdot)\) \(\chi_{1309}(388,\cdot)\) \(\chi_{1309}(411,\cdot)\) \(\chi_{1309}(432,\cdot)\) \(\chi_{1309}(465,\cdot)\) \(\chi_{1309}(488,\cdot)\) \(\chi_{1309}(500,\cdot)\) \(\chi_{1309}(521,\cdot)\) \(\chi_{1309}(537,\cdot)\) \(\chi_{1309}(598,\cdot)\) \(\chi_{1309}(619,\cdot)\) ...

Related number fields

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

Values on generators

\((1123,596,309)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{3}{5}\right),e\left(\frac{9}{16}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(8\)	\(9\)	\(10\)	\(12\)	\(13\)
\( \chi_{ 1309 }(31, a) \)	\(1\)	\(1\)	\(e\left(\frac{97}{120}\right)\)	\(e\left(\frac{127}{240}\right)\)	\(e\left(\frac{37}{60}\right)\)	\(e\left(\frac{11}{240}\right)\)	\(e\left(\frac{27}{80}\right)\)	\(e\left(\frac{17}{40}\right)\)	\(e\left(\frac{7}{120}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{7}{20}\right)\)