Dirichlet character \(\chi_{2784}(683,\cdot)\)

• Label: 2784.683
• Modulus: $2784$
• Conductor: $2784$
• Order: $56$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(2784\)
Conductor:	\(2784\)
Order:	\(56\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 2784.eh

\(\chi_{2784}(83,\cdot)\) \(\chi_{2784}(107,\cdot)\) \(\chi_{2784}(227,\cdot)\) \(\chi_{2784}(371,\cdot)\) \(\chi_{2784}(587,\cdot)\) \(\chi_{2784}(683,\cdot)\) \(\chi_{2784}(779,\cdot)\) \(\chi_{2784}(803,\cdot)\) \(\chi_{2784}(923,\cdot)\) \(\chi_{2784}(1067,\cdot)\) \(\chi_{2784}(1283,\cdot)\) \(\chi_{2784}(1379,\cdot)\) \(\chi_{2784}(1475,\cdot)\) \(\chi_{2784}(1499,\cdot)\) \(\chi_{2784}(1619,\cdot)\) \(\chi_{2784}(1763,\cdot)\) \(\chi_{2784}(1979,\cdot)\) \(\chi_{2784}(2075,\cdot)\) \(\chi_{2784}(2171,\cdot)\) \(\chi_{2784}(2195,\cdot)\) \(\chi_{2784}(2315,\cdot)\) \(\chi_{2784}(2459,\cdot)\) \(\chi_{2784}(2675,\cdot)\) \(\chi_{2784}(2771,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{56})$
Fixed field:	Number field defined by a degree 56 polynomial

Values on generators

\((1567,2437,929,1249)\) → \((-1,e\left(\frac{5}{8}\right),-1,e\left(\frac{1}{7}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(31\)	\(35\)
\( \chi_{ 2784 }(683, a) \)	\(1\)	\(1\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{13}{28}\right)\)	\(e\left(\frac{39}{56}\right)\)	\(e\left(\frac{53}{56}\right)\)	\(1\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{17}{28}\right)\)	\(e\left(\frac{15}{28}\right)\)	\(e\left(\frac{9}{14}\right)\)	\(e\left(\frac{41}{56}\right)\)