Dirichlet character \(\chi_{3328}(163,\cdot)\)

• Label: 3328.163
• Modulus: $3328$
• Conductor: $3328$
• Order: $192$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(3328\)
Conductor:	\(3328\)
Order:	\(192\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 3328.dt

\(\chi_{3328}(115,\cdot)\) \(\chi_{3328}(123,\cdot)\) \(\chi_{3328}(163,\cdot)\) \(\chi_{3328}(171,\cdot)\) \(\chi_{3328}(323,\cdot)\) \(\chi_{3328}(331,\cdot)\) \(\chi_{3328}(371,\cdot)\) \(\chi_{3328}(379,\cdot)\) \(\chi_{3328}(531,\cdot)\) \(\chi_{3328}(539,\cdot)\) \(\chi_{3328}(579,\cdot)\) \(\chi_{3328}(587,\cdot)\) \(\chi_{3328}(739,\cdot)\) \(\chi_{3328}(747,\cdot)\) \(\chi_{3328}(787,\cdot)\) \(\chi_{3328}(795,\cdot)\) \(\chi_{3328}(947,\cdot)\) \(\chi_{3328}(955,\cdot)\) \(\chi_{3328}(995,\cdot)\) \(\chi_{3328}(1003,\cdot)\) \(\chi_{3328}(1155,\cdot)\) \(\chi_{3328}(1163,\cdot)\) \(\chi_{3328}(1203,\cdot)\) \(\chi_{3328}(1211,\cdot)\) \(\chi_{3328}(1363,\cdot)\) \(\chi_{3328}(1371,\cdot)\) \(\chi_{3328}(1411,\cdot)\) \(\chi_{3328}(1419,\cdot)\) \(\chi_{3328}(1571,\cdot)\) \(\chi_{3328}(1579,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{192})$
Fixed field:	Number field defined by a degree 192 polynomial (not computed)

Values on generators

\((1535,261,769)\) → \((-1,e\left(\frac{43}{64}\right),e\left(\frac{11}{12}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 3328 }(163, a) \)	\(1\)	\(1\)	\(e\left(\frac{131}{192}\right)\)	\(e\left(\frac{59}{64}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{5}{192}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{103}{192}\right)\)	\(e\left(\frac{63}{64}\right)\)	\(e\left(\frac{7}{96}\right)\)