Dirichlet character \(\chi_{4729}(117,\cdot)\)

• Label: 4729.117
• Modulus: $4729$
• Conductor: $4729$
• Order: $591$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4729\)
Conductor:	\(4729\)
Order:	\(591\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4729.k

\(\chi_{4729}(14,\cdot)\) \(\chi_{4729}(19,\cdot)\) \(\chi_{4729}(21,\cdot)\) \(\chi_{4729}(35,\cdot)\) \(\chi_{4729}(37,\cdot)\) \(\chi_{4729}(40,\cdot)\) \(\chi_{4729}(52,\cdot)\) \(\chi_{4729}(60,\cdot)\) \(\chi_{4729}(67,\cdot)\) \(\chi_{4729}(78,\cdot)\) \(\chi_{4729}(83,\cdot)\) \(\chi_{4729}(90,\cdot)\) \(\chi_{4729}(100,\cdot)\) \(\chi_{4729}(117,\cdot)\) \(\chi_{4729}(118,\cdot)\) \(\chi_{4729}(130,\cdot)\) \(\chi_{4729}(131,\cdot)\) \(\chi_{4729}(135,\cdot)\) \(\chi_{4729}(150,\cdot)\) \(\chi_{4729}(169,\cdot)\) \(\chi_{4729}(177,\cdot)\) \(\chi_{4729}(187,\cdot)\) \(\chi_{4729}(193,\cdot)\) \(\chi_{4729}(195,\cdot)\) \(\chi_{4729}(196,\cdot)\) \(\chi_{4729}(224,\cdot)\) \(\chi_{4729}(225,\cdot)\) \(\chi_{4729}(266,\cdot)\) \(\chi_{4729}(294,\cdot)\) \(\chi_{4729}(304,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{591})$
Fixed field:	Number field defined by a degree 591 polynomial (not computed)

Values on generators

\(17\) → \(e\left(\frac{425}{591}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 4729 }(117, a) \)	\(1\)	\(1\)	\(e\left(\frac{134}{197}\right)\)	\(e\left(\frac{115}{197}\right)\)	\(e\left(\frac{71}{197}\right)\)	\(e\left(\frac{20}{591}\right)\)	\(e\left(\frac{52}{197}\right)\)	\(e\left(\frac{320}{591}\right)\)	\(e\left(\frac{8}{197}\right)\)	\(e\left(\frac{33}{197}\right)\)	\(e\left(\frac{422}{591}\right)\)	\(e\left(\frac{127}{197}\right)\)