Dirichlet character \(\chi_{4056}(5,\cdot)\)

• Label: 4056.5
• Modulus: $4056$
• Conductor: $4056$
• Order: $52$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4056\)
Conductor:	\(4056\)
Order:	\(52\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4056.cp

\(\chi_{4056}(5,\cdot)\) \(\chi_{4056}(125,\cdot)\) \(\chi_{4056}(317,\cdot)\) \(\chi_{4056}(629,\cdot)\) \(\chi_{4056}(749,\cdot)\) \(\chi_{4056}(941,\cdot)\) \(\chi_{4056}(1061,\cdot)\) \(\chi_{4056}(1373,\cdot)\) \(\chi_{4056}(1565,\cdot)\) \(\chi_{4056}(1685,\cdot)\) \(\chi_{4056}(1877,\cdot)\) \(\chi_{4056}(1997,\cdot)\) \(\chi_{4056}(2189,\cdot)\) \(\chi_{4056}(2309,\cdot)\) \(\chi_{4056}(2501,\cdot)\) \(\chi_{4056}(2621,\cdot)\) \(\chi_{4056}(2813,\cdot)\) \(\chi_{4056}(2933,\cdot)\) \(\chi_{4056}(3125,\cdot)\) \(\chi_{4056}(3245,\cdot)\) \(\chi_{4056}(3437,\cdot)\) \(\chi_{4056}(3557,\cdot)\) \(\chi_{4056}(3749,\cdot)\) \(\chi_{4056}(3869,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{52})$
Fixed field:	Number field defined by a degree 52 polynomial

Values on generators

\((1015,2029,2705,3889)\) → \((1,-1,-1,e\left(\frac{3}{52}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 4056 }(5, a) \)	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{9}{52}\right)\)	\(e\left(\frac{49}{52}\right)\)	\(e\left(\frac{12}{13}\right)\)	\(i\)	\(1\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{4}{13}\right)\)	\(e\left(\frac{11}{52}\right)\)	\(e\left(\frac{9}{13}\right)\)