Dirichlet character \(\chi_{9984}(419,\cdot)\)

• Label: 9984.419
• 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.hp

\(\chi_{9984}(35,\cdot)\) \(\chi_{9984}(107,\cdot)\) \(\chi_{9984}(347,\cdot)\) \(\chi_{9984}(419,\cdot)\) \(\chi_{9984}(659,\cdot)\) \(\chi_{9984}(731,\cdot)\) \(\chi_{9984}(971,\cdot)\) \(\chi_{9984}(1043,\cdot)\) \(\chi_{9984}(1283,\cdot)\) \(\chi_{9984}(1355,\cdot)\) \(\chi_{9984}(1595,\cdot)\) \(\chi_{9984}(1667,\cdot)\) \(\chi_{9984}(1907,\cdot)\) \(\chi_{9984}(1979,\cdot)\) \(\chi_{9984}(2219,\cdot)\) \(\chi_{9984}(2291,\cdot)\) \(\chi_{9984}(2531,\cdot)\) \(\chi_{9984}(2603,\cdot)\) \(\chi_{9984}(2843,\cdot)\) \(\chi_{9984}(2915,\cdot)\) \(\chi_{9984}(3155,\cdot)\) \(\chi_{9984}(3227,\cdot)\) \(\chi_{9984}(3467,\cdot)\) \(\chi_{9984}(3539,\cdot)\) \(\chi_{9984}(3779,\cdot)\) \(\chi_{9984}(3851,\cdot)\) \(\chi_{9984}(4091,\cdot)\) \(\chi_{9984}(4163,\cdot)\) \(\chi_{9984}(4403,\cdot)\) \(\chi_{9984}(4475,\cdot)\) ...

Related number fields

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

Values on generators

\((8191,3589,3329,769)\) → \((-1,e\left(\frac{43}{64}\right),-1,e\left(\frac{1}{3}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\( \chi_{ 9984 }(419, a) \)	\(1\)	\(1\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{85}{192}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{119}{192}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{91}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{11}{192}\right)\)