Dirichlet character \(\chi_{8004}(3659,\cdot)\)

• Label: 8004.3659
• 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.cv

\(\chi_{8004}(35,\cdot)\) \(\chi_{8004}(71,\cdot)\) \(\chi_{8004}(167,\cdot)\) \(\chi_{8004}(179,\cdot)\) \(\chi_{8004}(515,\cdot)\) \(\chi_{8004}(647,\cdot)\) \(\chi_{8004}(671,\cdot)\) \(\chi_{8004}(731,\cdot)\) \(\chi_{8004}(767,\cdot)\) \(\chi_{8004}(863,\cdot)\) \(\chi_{8004}(995,\cdot)\) \(\chi_{8004}(1223,\cdot)\) \(\chi_{8004}(1343,\cdot)\) \(\chi_{8004}(1559,\cdot)\) \(\chi_{8004}(1691,\cdot)\) \(\chi_{8004}(1715,\cdot)\) \(\chi_{8004}(1775,\cdot)\) \(\chi_{8004}(2063,\cdot)\) \(\chi_{8004}(2267,\cdot)\) \(\chi_{8004}(2387,\cdot)\) \(\chi_{8004}(2603,\cdot)\) \(\chi_{8004}(2615,\cdot)\) \(\chi_{8004}(2819,\cdot)\) \(\chi_{8004}(2855,\cdot)\) \(\chi_{8004}(3107,\cdot)\) \(\chi_{8004}(3167,\cdot)\) \(\chi_{8004}(3203,\cdot)\) \(\chi_{8004}(3431,\cdot)\) \(\chi_{8004}(3551,\cdot)\) \(\chi_{8004}(3647,\cdot)\) ...

Related number fields

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

Values on generators

\((4003,2669,3133,553)\) → \((-1,-1,e\left(\frac{1}{11}\right),e\left(\frac{11}{14}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(25\)	\(31\)	\(35\)	\(37\)
\( \chi_{ 8004 }(3659, a) \)	\(1\)	\(1\)	\(e\left(\frac{135}{154}\right)\)	\(e\left(\frac{101}{154}\right)\)	\(e\left(\frac{71}{154}\right)\)	\(e\left(\frac{32}{77}\right)\)	\(e\left(\frac{7}{11}\right)\)	\(e\left(\frac{72}{77}\right)\)	\(e\left(\frac{58}{77}\right)\)	\(e\left(\frac{64}{77}\right)\)	\(e\left(\frac{41}{77}\right)\)	\(e\left(\frac{41}{154}\right)\)