Dirichlet character \(\chi_{8112}(821,\cdot)\)

• Label: 8112.821
• 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.gd

\(\chi_{8112}(149,\cdot)\) \(\chi_{8112}(197,\cdot)\) \(\chi_{8112}(557,\cdot)\) \(\chi_{8112}(605,\cdot)\) \(\chi_{8112}(773,\cdot)\) \(\chi_{8112}(821,\cdot)\) \(\chi_{8112}(1181,\cdot)\) \(\chi_{8112}(1229,\cdot)\) \(\chi_{8112}(1397,\cdot)\) \(\chi_{8112}(1445,\cdot)\) \(\chi_{8112}(1805,\cdot)\) \(\chi_{8112}(1853,\cdot)\) \(\chi_{8112}(2021,\cdot)\) \(\chi_{8112}(2069,\cdot)\) \(\chi_{8112}(2429,\cdot)\) \(\chi_{8112}(2477,\cdot)\) \(\chi_{8112}(2645,\cdot)\) \(\chi_{8112}(2693,\cdot)\) \(\chi_{8112}(3053,\cdot)\) \(\chi_{8112}(3101,\cdot)\) \(\chi_{8112}(3269,\cdot)\) \(\chi_{8112}(3317,\cdot)\) \(\chi_{8112}(3677,\cdot)\) \(\chi_{8112}(3725,\cdot)\) \(\chi_{8112}(3893,\cdot)\) \(\chi_{8112}(3941,\cdot)\) \(\chi_{8112}(4301,\cdot)\) \(\chi_{8112}(4349,\cdot)\) \(\chi_{8112}(4517,\cdot)\) \(\chi_{8112}(4565,\cdot)\) ...

Related number fields

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

Values on generators

\((5071,6085,2705,3889)\) → \((1,i,-1,e\left(\frac{49}{156}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 8112 }(821, a) \)	\(1\)	\(1\)	\(e\left(\frac{15}{26}\right)\)	\(e\left(\frac{17}{156}\right)\)	\(e\left(\frac{4}{39}\right)\)	\(e\left(\frac{14}{39}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{2}{13}\right)\)	\(e\left(\frac{127}{156}\right)\)	\(e\left(\frac{31}{52}\right)\)	\(e\left(\frac{107}{156}\right)\)