Dirichlet character \(\chi_{31768}(18765,\cdot)\)

• Label: 31768.18765
• Modulus: $31768$
• Conductor: $31768$
• Order: $114$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(31768\)
Conductor:	\(31768\)
Order:	\(114\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 31768.eu

\(\chi_{31768}(373,\cdot)\) \(\chi_{31768}(901,\cdot)\) \(\chi_{31768}(2045,\cdot)\) \(\chi_{31768}(2573,\cdot)\) \(\chi_{31768}(3717,\cdot)\) \(\chi_{31768}(4245,\cdot)\) \(\chi_{31768}(5389,\cdot)\) \(\chi_{31768}(5917,\cdot)\) \(\chi_{31768}(7061,\cdot)\) \(\chi_{31768}(7589,\cdot)\) \(\chi_{31768}(9261,\cdot)\) \(\chi_{31768}(10405,\cdot)\) \(\chi_{31768}(10933,\cdot)\) \(\chi_{31768}(12077,\cdot)\) \(\chi_{31768}(12605,\cdot)\) \(\chi_{31768}(13749,\cdot)\) \(\chi_{31768}(14277,\cdot)\) \(\chi_{31768}(15421,\cdot)\) \(\chi_{31768}(15949,\cdot)\) \(\chi_{31768}(17093,\cdot)\) \(\chi_{31768}(18765,\cdot)\) \(\chi_{31768}(19293,\cdot)\) \(\chi_{31768}(20437,\cdot)\) \(\chi_{31768}(20965,\cdot)\) \(\chi_{31768}(22109,\cdot)\) \(\chi_{31768}(22637,\cdot)\) \(\chi_{31768}(23781,\cdot)\) \(\chi_{31768}(24309,\cdot)\) \(\chi_{31768}(25453,\cdot)\) \(\chi_{31768}(25981,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{57})$
Fixed field:	Number field defined by a degree 114 polynomial (not computed)

Values on generators

\((7943,15885,5777,14081)\) → \((1,-1,-1,e\left(\frac{107}{114}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\( \chi_{ 31768 }(18765, a) \)	\(1\)	\(1\)	\(e\left(\frac{55}{57}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{11}{38}\right)\)	\(e\left(\frac{53}{57}\right)\)	\(e\left(\frac{91}{114}\right)\)	\(e\left(\frac{25}{114}\right)\)	\(e\left(\frac{71}{114}\right)\)	\(e\left(\frac{29}{114}\right)\)	\(e\left(\frac{2}{57}\right)\)	\(e\left(\frac{29}{57}\right)\)