Dirichlet character \(\chi_{4598}(65,\cdot)\)

• Label: 4598.65
• Modulus: $4598$
• Conductor: $2299$
• Order: $66$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4598\)
Conductor:	\(2299\)
Order:	\(66\)
Real:	no
Primitive:	no, induced from \(\chi_{2299}(65,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 4598.bd

\(\chi_{4598}(65,\cdot)\) \(\chi_{4598}(373,\cdot)\) \(\chi_{4598}(791,\cdot)\) \(\chi_{4598}(901,\cdot)\) \(\chi_{4598}(1319,\cdot)\) \(\chi_{4598}(1627,\cdot)\) \(\chi_{4598}(1737,\cdot)\) \(\chi_{4598}(2045,\cdot)\) \(\chi_{4598}(2155,\cdot)\) \(\chi_{4598}(2463,\cdot)\) \(\chi_{4598}(2573,\cdot)\) \(\chi_{4598}(2881,\cdot)\) \(\chi_{4598}(2991,\cdot)\) \(\chi_{4598}(3299,\cdot)\) \(\chi_{4598}(3409,\cdot)\) \(\chi_{4598}(3717,\cdot)\) \(\chi_{4598}(3827,\cdot)\) \(\chi_{4598}(4135,\cdot)\) \(\chi_{4598}(4245,\cdot)\) \(\chi_{4598}(4553,\cdot)\)

Related number fields

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

Values on generators

\((3269,3631)\) → \((e\left(\frac{13}{22}\right),e\left(\frac{1}{6}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\( \chi_{ 4598 }(65, a) \)	\(1\)	\(1\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{33}\right)\)	\(e\left(\frac{3}{22}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{37}{66}\right)\)	\(e\left(\frac{41}{66}\right)\)	\(e\left(\frac{10}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{26}{33}\right)\)