Dirichlet character \(\chi_{8664}(173,\cdot)\)

• Label: 8664.173
• Modulus: $8664$
• Conductor: $8664$
• Order: $342$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8664\)
Conductor:	\(8664\)
Order:	\(342\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8664.dp

\(\chi_{8664}(29,\cdot)\) \(\chi_{8664}(53,\cdot)\) \(\chi_{8664}(173,\cdot)\) \(\chi_{8664}(269,\cdot)\) \(\chi_{8664}(317,\cdot)\) \(\chi_{8664}(413,\cdot)\) \(\chi_{8664}(485,\cdot)\) \(\chi_{8664}(509,\cdot)\) \(\chi_{8664}(629,\cdot)\) \(\chi_{8664}(725,\cdot)\) \(\chi_{8664}(773,\cdot)\) \(\chi_{8664}(869,\cdot)\) \(\chi_{8664}(941,\cdot)\) \(\chi_{8664}(965,\cdot)\) \(\chi_{8664}(1085,\cdot)\) \(\chi_{8664}(1181,\cdot)\) \(\chi_{8664}(1229,\cdot)\) \(\chi_{8664}(1325,\cdot)\) \(\chi_{8664}(1397,\cdot)\) \(\chi_{8664}(1421,\cdot)\) \(\chi_{8664}(1541,\cdot)\) \(\chi_{8664}(1637,\cdot)\) \(\chi_{8664}(1685,\cdot)\) \(\chi_{8664}(1781,\cdot)\) \(\chi_{8664}(1853,\cdot)\) \(\chi_{8664}(1877,\cdot)\) \(\chi_{8664}(1997,\cdot)\) \(\chi_{8664}(2093,\cdot)\) \(\chi_{8664}(2141,\cdot)\) \(\chi_{8664}(2237,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{171})$
Fixed field:	Number field defined by a degree 342 polynomial (not computed)

Values on generators

\((2167,4333,5777,8305)\) → \((1,-1,-1,e\left(\frac{199}{342}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 8664 }(173, a) \)	\(1\)	\(1\)	\(e\left(\frac{170}{171}\right)\)	\(e\left(\frac{16}{57}\right)\)	\(e\left(\frac{20}{57}\right)\)	\(e\left(\frac{160}{171}\right)\)	\(e\left(\frac{1}{342}\right)\)	\(e\left(\frac{155}{342}\right)\)	\(e\left(\frac{169}{171}\right)\)	\(e\left(\frac{305}{342}\right)\)	\(e\left(\frac{35}{114}\right)\)	\(e\left(\frac{47}{171}\right)\)