Dirichlet character \(\chi_{2557}(42,\cdot)\)

• Label: 2557.42
• Modulus: $2557$
• Conductor: $2557$
• Order: $2556$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

Modulus:	\(2557\)
Conductor:	\(2557\)
Order:	\(2556\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	odd

Galois orbit 2557.r

\(\chi_{2557}(2,\cdot)\) \(\chi_{2557}(5,\cdot)\) \(\chi_{2557}(6,\cdot)\) \(\chi_{2557}(15,\cdot)\) \(\chi_{2557}(17,\cdot)\) \(\chi_{2557}(24,\cdot)\) \(\chi_{2557}(31,\cdot)\) \(\chi_{2557}(32,\cdot)\) \(\chi_{2557}(41,\cdot)\) \(\chi_{2557}(42,\cdot)\) \(\chi_{2557}(43,\cdot)\) \(\chi_{2557}(47,\cdot)\) \(\chi_{2557}(51,\cdot)\) \(\chi_{2557}(54,\cdot)\) \(\chi_{2557}(56,\cdot)\) \(\chi_{2557}(60,\cdot)\) \(\chi_{2557}(66,\cdot)\) \(\chi_{2557}(67,\cdot)\) \(\chi_{2557}(72,\cdot)\) \(\chi_{2557}(78,\cdot)\) \(\chi_{2557}(80,\cdot)\) \(\chi_{2557}(83,\cdot)\) \(\chi_{2557}(88,\cdot)\) \(\chi_{2557}(89,\cdot)\) \(\chi_{2557}(98,\cdot)\) \(\chi_{2557}(103,\cdot)\) \(\chi_{2557}(104,\cdot)\) \(\chi_{2557}(105,\cdot)\) \(\chi_{2557}(106,\cdot)\) \(\chi_{2557}(107,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{2556})$
Fixed field:	Number field defined by a degree 2556 polynomial (not computed)

Values on generators

\(2\) → \(e\left(\frac{1867}{2556}\right)\)

First values

\(a\)	\(-1\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(6\)	\(7\)	\(8\)	\(9\)	\(10\)	\(11\)
\( \chi_{ 2557 }(42, a) \)	\(-1\)	\(1\)	\(e\left(\frac{1867}{2556}\right)\)	\(e\left(\frac{283}{639}\right)\)	\(e\left(\frac{589}{1278}\right)\)	\(e\left(\frac{2221}{2556}\right)\)	\(e\left(\frac{443}{2556}\right)\)	\(e\left(\frac{709}{1278}\right)\)	\(e\left(\frac{163}{852}\right)\)	\(e\left(\frac{566}{639}\right)\)	\(e\left(\frac{383}{639}\right)\)	\(e\left(\frac{455}{639}\right)\)