Dirichlet character \(\chi_{4598}(45,\cdot)\)

• Label: 4598.45
• Modulus: $4598$
• Conductor: $2299$
• Order: $33$
• Real: no
• Primitive: no
• Minimal: yes
• Parity: even

Basic properties

Modulus:	\(4598\)
Conductor:	\(2299\)
Order:	\(33\)
Real:	no
Primitive:	no, induced from \(\chi_{2299}(45,\cdot)\)
Minimal:	yes
Parity:	even

Galois orbit 4598.y

\(\chi_{4598}(45,\cdot)\) \(\chi_{4598}(353,\cdot)\) \(\chi_{4598}(463,\cdot)\) \(\chi_{4598}(771,\cdot)\) \(\chi_{4598}(881,\cdot)\) \(\chi_{4598}(1189,\cdot)\) \(\chi_{4598}(1299,\cdot)\) \(\chi_{4598}(1607,\cdot)\) \(\chi_{4598}(1717,\cdot)\) \(\chi_{4598}(2025,\cdot)\) \(\chi_{4598}(2135,\cdot)\) \(\chi_{4598}(2443,\cdot)\) \(\chi_{4598}(2553,\cdot)\) \(\chi_{4598}(2861,\cdot)\) \(\chi_{4598}(2971,\cdot)\) \(\chi_{4598}(3279,\cdot)\) \(\chi_{4598}(3697,\cdot)\) \(\chi_{4598}(3807,\cdot)\) \(\chi_{4598}(4225,\cdot)\) \(\chi_{4598}(4533,\cdot)\)

Related number fields

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

Values on generators

\((3269,3631)\) → \((e\left(\frac{3}{11}\right),e\left(\frac{1}{3}\right))\)

First values

\(a\)	\(-1\)	\(1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(13\)	\(15\)	\(17\)	\(21\)	\(23\)	\(25\)
\( \chi_{ 4598 }(45, a) \)	\(1\)	\(1\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{17}{33}\right)\)	\(e\left(\frac{10}{11}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{7}{33}\right)\)	\(e\left(\frac{28}{33}\right)\)	\(e\left(\frac{23}{33}\right)\)	\(e\left(\frac{8}{33}\right)\)	\(e\left(\frac{25}{33}\right)\)	\(e\left(\frac{1}{33}\right)\)