Dirichlet character \(\chi_{2784}(2069,\cdot)\)

• Label: 2784.2069
• 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.ed

\(\chi_{2784}(77,\cdot)\) \(\chi_{2784}(677,\cdot)\) \(\chi_{2784}(797,\cdot)\) \(\chi_{2784}(917,\cdot)\) \(\chi_{2784}(965,\cdot)\) \(\chi_{2784}(989,\cdot)\) \(\chi_{2784}(1013,\cdot)\) \(\chi_{2784}(1133,\cdot)\) \(\chi_{2784}(1157,\cdot)\) \(\chi_{2784}(1181,\cdot)\) \(\chi_{2784}(1229,\cdot)\) \(\chi_{2784}(1349,\cdot)\) \(\chi_{2784}(1469,\cdot)\) \(\chi_{2784}(2069,\cdot)\) \(\chi_{2784}(2189,\cdot)\) \(\chi_{2784}(2309,\cdot)\) \(\chi_{2784}(2357,\cdot)\) \(\chi_{2784}(2381,\cdot)\) \(\chi_{2784}(2405,\cdot)\) \(\chi_{2784}(2525,\cdot)\) \(\chi_{2784}(2549,\cdot)\) \(\chi_{2784}(2573,\cdot)\) \(\chi_{2784}(2621,\cdot)\) \(\chi_{2784}(2741,\cdot)\)

Related number fields

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

Values on generators

\((1567,2437,929,1249)\) → \((1,e\left(\frac{5}{8}\right),-1,e\left(\frac{23}{28}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(31\)	\(35\)
\( \chi_{ 2784 }(2069, a) \)	\(1\)	\(1\)	\(e\left(\frac{11}{56}\right)\)	\(e\left(\frac{3}{28}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(e\left(\frac{9}{56}\right)\)	\(i\)	\(e\left(\frac{43}{56}\right)\)	\(e\left(\frac{19}{28}\right)\)	\(e\left(\frac{11}{28}\right)\)	\(e\left(\frac{23}{28}\right)\)	\(e\left(\frac{17}{56}\right)\)