Dirichlet character \(\chi_{2704}(2133,\cdot)\)

• Label: 2704.2133
• Modulus: $2704$
• Conductor: $2704$
• Order: $52$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2704\)
Conductor:	\(2704\)
Order:	\(52\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2704.cd

\(\chi_{2704}(53,\cdot)\) \(\chi_{2704}(157,\cdot)\) \(\chi_{2704}(261,\cdot)\) \(\chi_{2704}(365,\cdot)\) \(\chi_{2704}(469,\cdot)\) \(\chi_{2704}(573,\cdot)\) \(\chi_{2704}(781,\cdot)\) \(\chi_{2704}(885,\cdot)\) \(\chi_{2704}(989,\cdot)\) \(\chi_{2704}(1093,\cdot)\) \(\chi_{2704}(1197,\cdot)\) \(\chi_{2704}(1301,\cdot)\) \(\chi_{2704}(1405,\cdot)\) \(\chi_{2704}(1509,\cdot)\) \(\chi_{2704}(1613,\cdot)\) \(\chi_{2704}(1717,\cdot)\) \(\chi_{2704}(1821,\cdot)\) \(\chi_{2704}(1925,\cdot)\) \(\chi_{2704}(2133,\cdot)\) \(\chi_{2704}(2237,\cdot)\) \(\chi_{2704}(2341,\cdot)\) \(\chi_{2704}(2445,\cdot)\) \(\chi_{2704}(2549,\cdot)\) \(\chi_{2704}(2653,\cdot)\)

Related number fields

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

Values on generators

\((2367,677,1185)\) → \((1,i,e\left(\frac{7}{13}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 2704 }(2133, a) \)	\(1\)	\(1\)	\(e\left(\frac{27}{52}\right)\)	\(e\left(\frac{5}{52}\right)\)	\(e\left(\frac{3}{26}\right)\)	\(e\left(\frac{1}{26}\right)\)	\(e\left(\frac{37}{52}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(e\left(\frac{8}{13}\right)\)	\(-i\)	\(e\left(\frac{33}{52}\right)\)	\(-1\)