Dirichlet character \(\chi_{4729}(1061,\cdot)\)

• Label: 4729.1061
• Modulus: $4729$
• Conductor: $4729$
• Order: $2364$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4729\)
Conductor:	\(4729\)
Order:	\(2364\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4729.o

\(\chi_{4729}(5,\cdot)\) \(\chi_{4729}(7,\cdot)\) \(\chi_{4729}(20,\cdot)\) \(\chi_{4729}(26,\cdot)\) \(\chi_{4729}(28,\cdot)\) \(\chi_{4729}(30,\cdot)\) \(\chi_{4729}(38,\cdot)\) \(\chi_{4729}(39,\cdot)\) \(\chi_{4729}(42,\cdot)\) \(\chi_{4729}(45,\cdot)\) \(\chi_{4729}(50,\cdot)\) \(\chi_{4729}(57,\cdot)\) \(\chi_{4729}(59,\cdot)\) \(\chi_{4729}(63,\cdot)\) \(\chi_{4729}(65,\cdot)\) \(\chi_{4729}(70,\cdot)\) \(\chi_{4729}(71,\cdot)\) \(\chi_{4729}(73,\cdot)\) \(\chi_{4729}(74,\cdot)\) \(\chi_{4729}(75,\cdot)\) \(\chi_{4729}(80,\cdot)\) \(\chi_{4729}(91,\cdot)\) \(\chi_{4729}(95,\cdot)\) \(\chi_{4729}(98,\cdot)\) \(\chi_{4729}(104,\cdot)\) \(\chi_{4729}(105,\cdot)\) \(\chi_{4729}(111,\cdot)\) \(\chi_{4729}(112,\cdot)\) \(\chi_{4729}(120,\cdot)\) \(\chi_{4729}(133,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{2364})$
Fixed field:	Number field defined by a degree 2364 polynomial (not computed)

Values on generators

\(17\) → \(e\left(\frac{37}{2364}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 4729 }(1061, a) \)	\(1\)	\(1\)	\(e\left(\frac{385}{394}\right)\)	\(e\left(\frac{129}{394}\right)\)	\(e\left(\frac{188}{197}\right)\)	\(e\left(\frac{425}{1182}\right)\)	\(e\left(\frac{60}{197}\right)\)	\(e\left(\frac{299}{1182}\right)\)	\(e\left(\frac{367}{394}\right)\)	\(e\left(\frac{129}{197}\right)\)	\(e\left(\frac{199}{591}\right)\)	\(e\left(\frac{177}{788}\right)\)