Dirichlet character \(\chi_{9984}(245,\cdot)\)

• Label: 9984.245
• Modulus: $9984$
• Conductor: $9984$
• Order: $192$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(9984\)
Conductor:	\(9984\)
Order:	\(192\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 9984.hk

\(\chi_{9984}(245,\cdot)\) \(\chi_{9984}(293,\cdot)\) \(\chi_{9984}(461,\cdot)\) \(\chi_{9984}(509,\cdot)\) \(\chi_{9984}(869,\cdot)\) \(\chi_{9984}(917,\cdot)\) \(\chi_{9984}(1085,\cdot)\) \(\chi_{9984}(1133,\cdot)\) \(\chi_{9984}(1493,\cdot)\) \(\chi_{9984}(1541,\cdot)\) \(\chi_{9984}(1709,\cdot)\) \(\chi_{9984}(1757,\cdot)\) \(\chi_{9984}(2117,\cdot)\) \(\chi_{9984}(2165,\cdot)\) \(\chi_{9984}(2333,\cdot)\) \(\chi_{9984}(2381,\cdot)\) \(\chi_{9984}(2741,\cdot)\) \(\chi_{9984}(2789,\cdot)\) \(\chi_{9984}(2957,\cdot)\) \(\chi_{9984}(3005,\cdot)\) \(\chi_{9984}(3365,\cdot)\) \(\chi_{9984}(3413,\cdot)\) \(\chi_{9984}(3581,\cdot)\) \(\chi_{9984}(3629,\cdot)\) \(\chi_{9984}(3989,\cdot)\) \(\chi_{9984}(4037,\cdot)\) \(\chi_{9984}(4205,\cdot)\) \(\chi_{9984}(4253,\cdot)\) \(\chi_{9984}(4613,\cdot)\) \(\chi_{9984}(4661,\cdot)\) ...

Related number fields

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

Values on generators

\((8191,3589,3329,769)\) → \((1,e\left(\frac{21}{64}\right),-1,e\left(\frac{7}{12}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 9984 }(245, a) \)	\(1\)	\(1\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{91}{192}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{89}{192}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{37}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{149}{192}\right)\)