Dirichlet character \(\chi_{8712}(139,\cdot)\)

• Label: 8712.139
• Modulus: $8712$
• Conductor: $8712$
• Order: $330$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8712\)
Conductor:	\(8712\)
Order:	\(330\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8712.eq

\(\chi_{8712}(139,\cdot)\) \(\chi_{8712}(211,\cdot)\) \(\chi_{8712}(259,\cdot)\) \(\chi_{8712}(283,\cdot)\) \(\chi_{8712}(547,\cdot)\) \(\chi_{8712}(787,\cdot)\) \(\chi_{8712}(931,\cdot)\) \(\chi_{8712}(1003,\cdot)\) \(\chi_{8712}(1051,\cdot)\) \(\chi_{8712}(1075,\cdot)\) \(\chi_{8712}(1195,\cdot)\) \(\chi_{8712}(1267,\cdot)\) \(\chi_{8712}(1339,\cdot)\) \(\chi_{8712}(1579,\cdot)\) \(\chi_{8712}(1723,\cdot)\) \(\chi_{8712}(1795,\cdot)\) \(\chi_{8712}(1843,\cdot)\) \(\chi_{8712}(1867,\cdot)\) \(\chi_{8712}(1987,\cdot)\) \(\chi_{8712}(2059,\cdot)\) \(\chi_{8712}(2131,\cdot)\) \(\chi_{8712}(2371,\cdot)\) \(\chi_{8712}(2515,\cdot)\) \(\chi_{8712}(2587,\cdot)\) \(\chi_{8712}(2779,\cdot)\) \(\chi_{8712}(2851,\cdot)\) \(\chi_{8712}(2923,\cdot)\) \(\chi_{8712}(3163,\cdot)\) \(\chi_{8712}(3427,\cdot)\) \(\chi_{8712}(3451,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{165})$
Fixed field:	Number field defined by a degree 330 polynomial (not computed)

Values on generators

\((6535,4357,1937,5689)\) → \((-1,-1,e\left(\frac{1}{3}\right),e\left(\frac{67}{110}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 8712 }(139, a) \)	\(1\)	\(1\)	\(e\left(\frac{79}{330}\right)\)	\(e\left(\frac{16}{165}\right)\)	\(e\left(\frac{113}{165}\right)\)	\(e\left(\frac{93}{110}\right)\)	\(e\left(\frac{61}{110}\right)\)	\(e\left(\frac{53}{66}\right)\)	\(e\left(\frac{79}{165}\right)\)	\(e\left(\frac{31}{165}\right)\)	\(e\left(\frac{181}{330}\right)\)	\(e\left(\frac{37}{110}\right)\)