Dirichlet character \(\chi_{8004}(83,\cdot)\)

• Label: 8004.83
• Modulus: $8004$
• Conductor: $8004$
• Order: $154$
• Real: no
• Primitive: yes
• Minimal: yes
• Parity: odd

Basic properties

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

Galois orbit 8004.dh

\(\chi_{8004}(83,\cdot)\) \(\chi_{8004}(107,\cdot)\) \(\chi_{8004}(227,\cdot)\) \(\chi_{8004}(431,\cdot)\) \(\chi_{8004}(779,\cdot)\) \(\chi_{8004}(803,\cdot)\) \(\chi_{8004}(935,\cdot)\) \(\chi_{8004}(1031,\cdot)\) \(\chi_{8004}(1631,\cdot)\) \(\chi_{8004}(1763,\cdot)\) \(\chi_{8004}(1847,\cdot)\) \(\chi_{8004}(2075,\cdot)\) \(\chi_{8004}(2195,\cdot)\) \(\chi_{8004}(2315,\cdot)\) \(\chi_{8004}(2459,\cdot)\) \(\chi_{8004}(2675,\cdot)\) \(\chi_{8004}(2771,\cdot)\) \(\chi_{8004}(2867,\cdot)\) \(\chi_{8004}(3011,\cdot)\) \(\chi_{8004}(3023,\cdot)\) \(\chi_{8004}(3119,\cdot)\) \(\chi_{8004}(3239,\cdot)\) \(\chi_{8004}(3467,\cdot)\) \(\chi_{8004}(3503,\cdot)\) \(\chi_{8004}(3563,\cdot)\) \(\chi_{8004}(3815,\cdot)\) \(\chi_{8004}(3851,\cdot)\) \(\chi_{8004}(4055,\cdot)\) \(\chi_{8004}(4067,\cdot)\) \(\chi_{8004}(4283,\cdot)\) ...

Related number fields

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

Values on generators

\((4003,2669,3133,553)\) → \((-1,-1,e\left(\frac{21}{22}\right),e\left(\frac{4}{7}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(31\)	\(35\)	\(37\)
\( \chi_{ 8004 }(83, a) \)	\(-1\)	\(1\)	\(e\left(\frac{2}{77}\right)\)	\(e\left(\frac{38}{77}\right)\)	\(e\left(\frac{135}{154}\right)\)	\(e\left(\frac{50}{77}\right)\)	\(e\left(\frac{2}{11}\right)\)	\(e\left(\frac{74}{77}\right)\)	\(e\left(\frac{4}{77}\right)\)	\(e\left(\frac{123}{154}\right)\)	\(e\left(\frac{40}{77}\right)\)	\(e\left(\frac{117}{154}\right)\)