Dirichlet character \(\chi_{5082}(89,\cdot)\)

• Label: 5082.89
• Modulus: $5082$
• Conductor: $2541$
• Order: $66$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(5082\)
Conductor:	\(2541\)
Order:	\(66\)
Real:	no
Primitive:	no, induced from \(\chi_{2541}(89,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 5082.bw

\(\chi_{5082}(89,\cdot)\) \(\chi_{5082}(353,\cdot)\) \(\chi_{5082}(551,\cdot)\) \(\chi_{5082}(815,\cdot)\) \(\chi_{5082}(1013,\cdot)\) \(\chi_{5082}(1277,\cdot)\) \(\chi_{5082}(1475,\cdot)\) \(\chi_{5082}(1739,\cdot)\) \(\chi_{5082}(2201,\cdot)\) \(\chi_{5082}(2399,\cdot)\) \(\chi_{5082}(2861,\cdot)\) \(\chi_{5082}(3125,\cdot)\) \(\chi_{5082}(3323,\cdot)\) \(\chi_{5082}(3587,\cdot)\) \(\chi_{5082}(3785,\cdot)\) \(\chi_{5082}(4049,\cdot)\) \(\chi_{5082}(4247,\cdot)\) \(\chi_{5082}(4511,\cdot)\) \(\chi_{5082}(4709,\cdot)\) \(\chi_{5082}(4973,\cdot)\)

Related number fields

Field of values:	\(\Q(\zeta_{33})\)
Fixed field:	Number field defined by a degree 66 polynomial

Values on generators

\((3389,4357,2059)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{6}{11}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(5\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(37\)	\(41\)
\( \chi_{ 5082 }(89, a) \)	\(1\)	\(1\)	\(e\left(\frac{1}{33}\right)\)	\(e\left(\frac{13}{22}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{29}{66}\right)\)	\(e\left(\frac{23}{66}\right)\)	\(e\left(\frac{2}{33}\right)\)	\(e\left(\frac{17}{22}\right)\)	\(e\left(\frac{49}{66}\right)\)	\(e\left(\frac{19}{33}\right)\)	\(e\left(\frac{6}{11}\right)\)