Dirichlet character \(\chi_{4729}(254,\cdot)\)

• Label: 4729.254
• Modulus: $4729$
• Conductor: $4729$
• Order: $394$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4729\)
Conductor:	\(4729\)
Order:	\(394\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4729.j

\(\chi_{4729}(4,\cdot)\) \(\chi_{4729}(6,\cdot)\) \(\chi_{4729}(9,\cdot)\) \(\chi_{4729}(64,\cdot)\) \(\chi_{4729}(96,\cdot)\) \(\chi_{4729}(144,\cdot)\) \(\chi_{4729}(197,\cdot)\) \(\chi_{4729}(216,\cdot)\) \(\chi_{4729}(242,\cdot)\) \(\chi_{4729}(254,\cdot)\) \(\chi_{4729}(324,\cdot)\) \(\chi_{4729}(350,\cdot)\) \(\chi_{4729}(355,\cdot)\) \(\chi_{4729}(363,\cdot)\) \(\chi_{4729}(381,\cdot)\) \(\chi_{4729}(413,\cdot)\) \(\chi_{4729}(422,\cdot)\) \(\chi_{4729}(451,\cdot)\) \(\chi_{4729}(454,\cdot)\) \(\chi_{4729}(455,\cdot)\) \(\chi_{4729}(458,\cdot)\) \(\chi_{4729}(475,\cdot)\) \(\chi_{4729}(486,\cdot)\) \(\chi_{4729}(525,\cdot)\) \(\chi_{4729}(607,\cdot)\) \(\chi_{4729}(613,\cdot)\) \(\chi_{4729}(633,\cdot)\) \(\chi_{4729}(634,\cdot)\) \(\chi_{4729}(643,\cdot)\) \(\chi_{4729}(670,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{197})$
Fixed field:	Number field defined by a degree 394 polynomial (not computed)

Values on generators

\(17\) → \(e\left(\frac{129}{394}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 4729 }(254, a) \)	\(1\)	\(1\)	\(e\left(\frac{23}{197}\right)\)	\(e\left(\frac{130}{197}\right)\)	\(e\left(\frac{46}{197}\right)\)	\(e\left(\frac{156}{197}\right)\)	\(e\left(\frac{153}{197}\right)\)	\(e\left(\frac{132}{197}\right)\)	\(e\left(\frac{69}{197}\right)\)	\(e\left(\frac{63}{197}\right)\)	\(e\left(\frac{179}{197}\right)\)	\(e\left(\frac{73}{394}\right)\)