Dirichlet character \(\chi_{4729}(55,\cdot)\)

• Label: 4729.55
• Modulus: $4729$
• Conductor: $4729$
• Order: $4728$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(4729\)
Conductor:	\(4729\)
Order:	\(4728\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 4729.p

\(\chi_{4729}(17,\cdot)\) \(\chi_{4729}(34,\cdot)\) \(\chi_{4729}(43,\cdot)\) \(\chi_{4729}(47,\cdot)\) \(\chi_{4729}(51,\cdot)\) \(\chi_{4729}(53,\cdot)\) \(\chi_{4729}(55,\cdot)\) \(\chi_{4729}(61,\cdot)\) \(\chi_{4729}(68,\cdot)\) \(\chi_{4729}(77,\cdot)\) \(\chi_{4729}(85,\cdot)\) \(\chi_{4729}(86,\cdot)\) \(\chi_{4729}(89,\cdot)\) \(\chi_{4729}(94,\cdot)\) \(\chi_{4729}(101,\cdot)\) \(\chi_{4729}(102,\cdot)\) \(\chi_{4729}(106,\cdot)\) \(\chi_{4729}(107,\cdot)\) \(\chi_{4729}(109,\cdot)\) \(\chi_{4729}(110,\cdot)\) \(\chi_{4729}(115,\cdot)\) \(\chi_{4729}(119,\cdot)\) \(\chi_{4729}(122,\cdot)\) \(\chi_{4729}(129,\cdot)\) \(\chi_{4729}(136,\cdot)\) \(\chi_{4729}(139,\cdot)\) \(\chi_{4729}(141,\cdot)\) \(\chi_{4729}(143,\cdot)\) \(\chi_{4729}(145,\cdot)\) \(\chi_{4729}(153,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{4728})$
Fixed field:	Number field defined by a degree 4728 polynomial (not computed)

Values on generators

\(17\) → \(e\left(\frac{229}{4728}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 4729 }(55, a) \)	\(-1\)	\(1\)	\(e\left(\frac{317}{788}\right)\)	\(e\left(\frac{53}{788}\right)\)	\(e\left(\frac{317}{394}\right)\)	\(e\left(\frac{2279}{2364}\right)\)	\(e\left(\frac{185}{394}\right)\)	\(e\left(\frac{413}{2364}\right)\)	\(e\left(\frac{163}{788}\right)\)	\(e\left(\frac{53}{394}\right)\)	\(e\left(\frac{433}{1182}\right)\)	\(e\left(\frac{201}{1576}\right)\)