Dirichlet character \(\chi_{4176}(3317,\cdot)\)

• Label: 4176.3317
• Modulus: $4176$
• Conductor: $4176$
• Order: $84$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4176\)
Conductor:	\(4176\)
Order:	\(84\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 4176.fl

\(\chi_{4176}(101,\cdot)\) \(\chi_{4176}(221,\cdot)\) \(\chi_{4176}(293,\cdot)\) \(\chi_{4176}(317,\cdot)\) \(\chi_{4176}(437,\cdot)\) \(\chi_{4176}(461,\cdot)\) \(\chi_{4176}(533,\cdot)\) \(\chi_{4176}(653,\cdot)\) \(\chi_{4176}(1373,\cdot)\) \(\chi_{4176}(1613,\cdot)\) \(\chi_{4176}(1661,\cdot)\) \(\chi_{4176}(1685,\cdot)\) \(\chi_{4176}(1829,\cdot)\) \(\chi_{4176}(1877,\cdot)\) \(\chi_{4176}(2045,\cdot)\) \(\chi_{4176}(2165,\cdot)\) \(\chi_{4176}(2765,\cdot)\) \(\chi_{4176}(2885,\cdot)\) \(\chi_{4176}(3053,\cdot)\) \(\chi_{4176}(3101,\cdot)\) \(\chi_{4176}(3245,\cdot)\) \(\chi_{4176}(3269,\cdot)\) \(\chi_{4176}(3317,\cdot)\) \(\chi_{4176}(3557,\cdot)\)

Related number fields

Field of values:	$\Q(\zeta_{84})$
Fixed field:	Number field defined by a degree 84 polynomial

Values on generators

\((1567,1045,929,4033)\) → \((1,i,e\left(\frac{5}{6}\right),e\left(\frac{25}{28}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(31\)	\(35\)
\( \chi_{ 4176 }(3317, a) \)	\(1\)	\(1\)	\(e\left(\frac{5}{84}\right)\)	\(e\left(\frac{23}{42}\right)\)	\(e\left(\frac{17}{42}\right)\)	\(e\left(\frac{41}{84}\right)\)	\(i\)	\(e\left(\frac{11}{14}\right)\)	\(e\left(\frac{11}{21}\right)\)	\(e\left(\frac{5}{42}\right)\)	\(e\left(\frac{47}{84}\right)\)	\(e\left(\frac{17}{28}\right)\)