Dirichlet character \(\chi_{4729}(314,\cdot)\)

• Label: 4729.314
• Modulus: $4729$
• Conductor: $4729$
• Order: $197$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4729\)
Conductor:	\(4729\)
Order:	\(197\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4729.i

\(\chi_{4729}(16,\cdot)\) \(\chi_{4729}(24,\cdot)\) \(\chi_{4729}(36,\cdot)\) \(\chi_{4729}(54,\cdot)\) \(\chi_{4729}(81,\cdot)\) \(\chi_{4729}(250,\cdot)\) \(\chi_{4729}(251,\cdot)\) \(\chi_{4729}(253,\cdot)\) \(\chi_{4729}(256,\cdot)\) \(\chi_{4729}(295,\cdot)\) \(\chi_{4729}(314,\cdot)\) \(\chi_{4729}(319,\cdot)\) \(\chi_{4729}(325,\cdot)\) \(\chi_{4729}(375,\cdot)\) \(\chi_{4729}(384,\cdot)\) \(\chi_{4729}(471,\cdot)\) \(\chi_{4729}(490,\cdot)\) \(\chi_{4729}(497,\cdot)\) \(\chi_{4729}(576,\cdot)\) \(\chi_{4729}(637,\cdot)\) \(\chi_{4729}(665,\cdot)\) \(\chi_{4729}(682,\cdot)\) \(\chi_{4729}(734,\cdot)\) \(\chi_{4729}(735,\cdot)\) \(\chi_{4729}(739,\cdot)\) \(\chi_{4729}(746,\cdot)\) \(\chi_{4729}(788,\cdot)\) \(\chi_{4729}(821,\cdot)\) \(\chi_{4729}(857,\cdot)\) \(\chi_{4729}(864,\cdot)\) ...

Related number fields

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

Values on generators

\(17\) → \(e\left(\frac{138}{197}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 4729 }(314, a) \)	\(1\)	\(1\)	\(e\left(\frac{150}{197}\right)\)	\(e\left(\frac{17}{197}\right)\)	\(e\left(\frac{103}{197}\right)\)	\(e\left(\frac{178}{197}\right)\)	\(e\left(\frac{167}{197}\right)\)	\(e\left(\frac{90}{197}\right)\)	\(e\left(\frac{56}{197}\right)\)	\(e\left(\frac{34}{197}\right)\)	\(e\left(\frac{131}{197}\right)\)	\(e\left(\frac{101}{197}\right)\)