Dirichlet character \(\chi_{2784}(1715,\cdot)\)

• Label: 2784.1715
• 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.ds

\(\chi_{2784}(35,\cdot)\) \(\chi_{2784}(179,\cdot)\) \(\chi_{2784}(299,\cdot)\) \(\chi_{2784}(323,\cdot)\) \(\chi_{2784}(419,\cdot)\) \(\chi_{2784}(515,\cdot)\) \(\chi_{2784}(731,\cdot)\) \(\chi_{2784}(875,\cdot)\) \(\chi_{2784}(995,\cdot)\) \(\chi_{2784}(1019,\cdot)\) \(\chi_{2784}(1115,\cdot)\) \(\chi_{2784}(1211,\cdot)\) \(\chi_{2784}(1427,\cdot)\) \(\chi_{2784}(1571,\cdot)\) \(\chi_{2784}(1691,\cdot)\) \(\chi_{2784}(1715,\cdot)\) \(\chi_{2784}(1811,\cdot)\) \(\chi_{2784}(1907,\cdot)\) \(\chi_{2784}(2123,\cdot)\) \(\chi_{2784}(2267,\cdot)\) \(\chi_{2784}(2387,\cdot)\) \(\chi_{2784}(2411,\cdot)\) \(\chi_{2784}(2507,\cdot)\) \(\chi_{2784}(2603,\cdot)\)

Related number fields

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

Values on generators

\((1567,2437,929,1249)\) → \((-1,e\left(\frac{7}{8}\right),-1,e\left(\frac{1}{14}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(31\)	\(35\)
\( \chi_{ 2784 }(1715, a) \)	\(1\)	\(1\)	\(e\left(\frac{53}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{23}{56}\right)\)	\(-1\)	\(e\left(\frac{15}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{25}{28}\right)\)	\(e\left(\frac{4}{7}\right)\)	\(e\left(\frac{3}{56}\right)\)