Dirichlet character \(\chi_{3328}(693,\cdot)\)

• Label: 3328.693
• 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.dw

\(\chi_{3328}(69,\cdot)\) \(\chi_{3328}(101,\cdot)\) \(\chi_{3328}(173,\cdot)\) \(\chi_{3328}(205,\cdot)\) \(\chi_{3328}(277,\cdot)\) \(\chi_{3328}(309,\cdot)\) \(\chi_{3328}(381,\cdot)\) \(\chi_{3328}(413,\cdot)\) \(\chi_{3328}(485,\cdot)\) \(\chi_{3328}(517,\cdot)\) \(\chi_{3328}(589,\cdot)\) \(\chi_{3328}(621,\cdot)\) \(\chi_{3328}(693,\cdot)\) \(\chi_{3328}(725,\cdot)\) \(\chi_{3328}(797,\cdot)\) \(\chi_{3328}(829,\cdot)\) \(\chi_{3328}(901,\cdot)\) \(\chi_{3328}(933,\cdot)\) \(\chi_{3328}(1005,\cdot)\) \(\chi_{3328}(1037,\cdot)\) \(\chi_{3328}(1109,\cdot)\) \(\chi_{3328}(1141,\cdot)\) \(\chi_{3328}(1213,\cdot)\) \(\chi_{3328}(1245,\cdot)\) \(\chi_{3328}(1317,\cdot)\) \(\chi_{3328}(1349,\cdot)\) \(\chi_{3328}(1421,\cdot)\) \(\chi_{3328}(1453,\cdot)\) \(\chi_{3328}(1525,\cdot)\) \(\chi_{3328}(1557,\cdot)\) ...

Related number fields

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

Values on generators

\((1535,261,769)\) → \((1,e\left(\frac{37}{64}\right),e\left(\frac{1}{6}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(15\)	\(17\)	\(19\)	\(21\)	\(23\)
\( \chi_{ 3328 }(693, a) \)	\(1\)	\(1\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{59}{192}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{25}{192}\right)\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{73}{96}\right)\)