Dirichlet character \(\chi_{8004}(719,\cdot)\)

• Label: 8004.719
• Modulus: $8004$
• Conductor: $8004$
• Order: $154$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(8004\)
Conductor:	\(8004\)
Order:	\(154\)
Real:	no
Primitive:	yes
Minimal:	yes
Parity:	even

Galois orbit 8004.cy

\(\chi_{8004}(239,\cdot)\) \(\chi_{8004}(335,\cdot)\) \(\chi_{8004}(371,\cdot)\) \(\chi_{8004}(455,\cdot)\) \(\chi_{8004}(587,\cdot)\) \(\chi_{8004}(683,\cdot)\) \(\chi_{8004}(719,\cdot)\) \(\chi_{8004}(923,\cdot)\) \(\chi_{8004}(1067,\cdot)\) \(\chi_{8004}(1271,\cdot)\) \(\chi_{8004}(1283,\cdot)\) \(\chi_{8004}(1415,\cdot)\) \(\chi_{8004}(1475,\cdot)\) \(\chi_{8004}(1499,\cdot)\) \(\chi_{8004}(1619,\cdot)\) \(\chi_{8004}(1727,\cdot)\) \(\chi_{8004}(1823,\cdot)\) \(\chi_{8004}(1967,\cdot)\) \(\chi_{8004}(2111,\cdot)\) \(\chi_{8004}(2171,\cdot)\) \(\chi_{8004}(2327,\cdot)\) \(\chi_{8004}(2423,\cdot)\) \(\chi_{8004}(2519,\cdot)\) \(\chi_{8004}(2543,\cdot)\) \(\chi_{8004}(2663,\cdot)\) \(\chi_{8004}(2891,\cdot)\) \(\chi_{8004}(3155,\cdot)\) \(\chi_{8004}(3215,\cdot)\) \(\chi_{8004}(3371,\cdot)\) \(\chi_{8004}(3707,\cdot)\) ...

Related number fields

Field of values:	$\Q(\zeta_{77})$
Fixed field:	Number field defined by a degree 154 polynomial (not computed)

Values on generators

\((4003,2669,3133,553)\) → \((-1,-1,e\left(\frac{9}{11}\right),e\left(\frac{5}{7}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(31\)	\(35\)	\(37\)
\( \chi_{ 8004 }(719, a) \)	\(1\)	\(1\)	\(e\left(\frac{5}{154}\right)\)	\(e\left(\frac{95}{154}\right)\)	\(e\left(\frac{17}{77}\right)\)	\(e\left(\frac{24}{77}\right)\)	\(e\left(\frac{5}{22}\right)\)	\(e\left(\frac{31}{154}\right)\)	\(e\left(\frac{5}{77}\right)\)	\(e\left(\frac{19}{154}\right)\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{25}{77}\right)\)