Dirichlet character \(\chi_{8112}(2333,\cdot)\)

• Label: 8112.2333
• Modulus: $8112$
• Conductor: $8112$
• Order: $156$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8112\)
Conductor:	\(8112\)
Order:	\(156\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8112.fh

\(\chi_{8112}(245,\cdot)\) \(\chi_{8112}(293,\cdot)\) \(\chi_{8112}(461,\cdot)\) \(\chi_{8112}(509,\cdot)\) \(\chi_{8112}(869,\cdot)\) \(\chi_{8112}(917,\cdot)\) \(\chi_{8112}(1085,\cdot)\) \(\chi_{8112}(1133,\cdot)\) \(\chi_{8112}(1493,\cdot)\) \(\chi_{8112}(1541,\cdot)\) \(\chi_{8112}(1757,\cdot)\) \(\chi_{8112}(2165,\cdot)\) \(\chi_{8112}(2333,\cdot)\) \(\chi_{8112}(2381,\cdot)\) \(\chi_{8112}(2741,\cdot)\) \(\chi_{8112}(2789,\cdot)\) \(\chi_{8112}(2957,\cdot)\) \(\chi_{8112}(3005,\cdot)\) \(\chi_{8112}(3365,\cdot)\) \(\chi_{8112}(3413,\cdot)\) \(\chi_{8112}(3581,\cdot)\) \(\chi_{8112}(3989,\cdot)\) \(\chi_{8112}(4205,\cdot)\) \(\chi_{8112}(4253,\cdot)\) \(\chi_{8112}(4613,\cdot)\) \(\chi_{8112}(4661,\cdot)\) \(\chi_{8112}(4829,\cdot)\) \(\chi_{8112}(4877,\cdot)\) \(\chi_{8112}(5237,\cdot)\) \(\chi_{8112}(5285,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{156})$
Fixed field:	Number field defined by a degree 156 polynomial (not computed)

Values on generators

\((5071,6085,2705,3889)\) → \((1,-i,-1,e\left(\frac{149}{156}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 8112 }(2333, a) \)	\(1\)	\(1\)	\(e\left(\frac{11}{13}\right)\)	\(e\left(\frac{109}{156}\right)\)	\(e\left(\frac{49}{78}\right)\)	\(e\left(\frac{37}{39}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{9}{13}\right)\)	\(e\left(\frac{149}{156}\right)\)	\(e\left(\frac{3}{52}\right)\)	\(e\left(\frac{85}{156}\right)\)