Dirichlet character \(\chi_{4729}(48,\cdot)\)

• Label: 4729.48
• Modulus: $4729$
• Conductor: $4729$
• Order: $788$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4729\)
Conductor:	\(4729\)
Order:	\(788\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4729.l

\(\chi_{4729}(2,\cdot)\) \(\chi_{4729}(3,\cdot)\) \(\chi_{4729}(8,\cdot)\) \(\chi_{4729}(12,\cdot)\) \(\chi_{4729}(18,\cdot)\) \(\chi_{4729}(27,\cdot)\) \(\chi_{4729}(32,\cdot)\) \(\chi_{4729}(48,\cdot)\) \(\chi_{4729}(72,\cdot)\) \(\chi_{4729}(108,\cdot)\) \(\chi_{4729}(121,\cdot)\) \(\chi_{4729}(125,\cdot)\) \(\chi_{4729}(127,\cdot)\) \(\chi_{4729}(128,\cdot)\) \(\chi_{4729}(157,\cdot)\) \(\chi_{4729}(162,\cdot)\) \(\chi_{4729}(175,\cdot)\) \(\chi_{4729}(192,\cdot)\) \(\chi_{4729}(211,\cdot)\) \(\chi_{4729}(227,\cdot)\) \(\chi_{4729}(229,\cdot)\) \(\chi_{4729}(243,\cdot)\) \(\chi_{4729}(245,\cdot)\) \(\chi_{4729}(288,\cdot)\) \(\chi_{4729}(317,\cdot)\) \(\chi_{4729}(335,\cdot)\) \(\chi_{4729}(341,\cdot)\) \(\chi_{4729}(343,\cdot)\) \(\chi_{4729}(367,\cdot)\) \(\chi_{4729}(373,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{788})$
Fixed field:	Number field defined by a degree 788 polynomial (not computed)

Values on generators

\(17\) → \(e\left(\frac{109}{788}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 4729 }(48, a) \)	\(1\)	\(1\)	\(e\left(\frac{389}{394}\right)\)	\(e\left(\frac{203}{394}\right)\)	\(e\left(\frac{192}{197}\right)\)	\(e\left(\frac{283}{394}\right)\)	\(e\left(\frac{99}{197}\right)\)	\(e\left(\frac{391}{394}\right)\)	\(e\left(\frac{379}{394}\right)\)	\(e\left(\frac{6}{197}\right)\)	\(e\left(\frac{139}{197}\right)\)	\(e\left(\frac{755}{788}\right)\)