Dirichlet character \(\chi_{2509}(497,\cdot)\)

• Label: 2509.497
• Modulus: $2509$
• Conductor: $2509$
• Order: $192$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(2509\)
Conductor:	\(2509\)
Order:	\(192\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2509.ep

\(\chi_{2509}(22,\cdot)\) \(\chi_{2509}(146,\cdot)\) \(\chi_{2509}(152,\cdot)\) \(\chi_{2509}(159,\cdot)\) \(\chi_{2509}(178,\cdot)\) \(\chi_{2509}(237,\cdot)\) \(\chi_{2509}(308,\cdot)\) \(\chi_{2509}(360,\cdot)\) \(\chi_{2509}(412,\cdot)\) \(\chi_{2509}(464,\cdot)\) \(\chi_{2509}(497,\cdot)\) \(\chi_{2509}(549,\cdot)\) \(\chi_{2509}(594,\cdot)\) \(\chi_{2509}(620,\cdot)\) \(\chi_{2509}(640,\cdot)\) \(\chi_{2509}(692,\cdot)\) \(\chi_{2509}(750,\cdot)\) \(\chi_{2509}(789,\cdot)\) \(\chi_{2509}(809,\cdot)\) \(\chi_{2509}(874,\cdot)\) \(\chi_{2509}(913,\cdot)\) \(\chi_{2509}(984,\cdot)\) \(\chi_{2509}(1010,\cdot)\) \(\chi_{2509}(1017,\cdot)\) \(\chi_{2509}(1023,\cdot)\) \(\chi_{2509}(1056,\cdot)\) \(\chi_{2509}(1088,\cdot)\) \(\chi_{2509}(1101,\cdot)\) \(\chi_{2509}(1121,\cdot)\) \(\chi_{2509}(1153,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{192})$
Fixed field:	Number field defined by a degree 192 polynomial (not computed)

Values on generators

\((1159,391)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{89}{192}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 2509 }(497, a) \)	\(-1\)	\(1\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{3}{16}\right)\)	\(e\left(\frac{89}{192}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{107}{192}\right)\)	\(e\left(\frac{31}{192}\right)\)