Basic properties
| Modulus: | \(4598\) | |
| Conductor: | \(2299\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(990\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2299}(383,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4598.bt
\(\chi_{4598}(15,\cdot)\) \(\chi_{4598}(53,\cdot)\) \(\chi_{4598}(59,\cdot)\) \(\chi_{4598}(71,\cdot)\) \(\chi_{4598}(91,\cdot)\) \(\chi_{4598}(97,\cdot)\) \(\chi_{4598}(135,\cdot)\) \(\chi_{4598}(147,\cdot)\) \(\chi_{4598}(181,\cdot)\) \(\chi_{4598}(185,\cdot)\) \(\chi_{4598}(203,\cdot)\) \(\chi_{4598}(223,\cdot)\) \(\chi_{4598}(257,\cdot)\) \(\chi_{4598}(279,\cdot)\) \(\chi_{4598}(295,\cdot)\) \(\chi_{4598}(317,\cdot)\) \(\chi_{4598}(333,\cdot)\) \(\chi_{4598}(345,\cdot)\) \(\chi_{4598}(355,\cdot)\) \(\chi_{4598}(357,\cdot)\) \(\chi_{4598}(383,\cdot)\) \(\chi_{4598}(401,\cdot)\) \(\chi_{4598}(421,\cdot)\) \(\chi_{4598}(433,\cdot)\) \(\chi_{4598}(471,\cdot)\) \(\chi_{4598}(477,\cdot)\) \(\chi_{4598}(489,\cdot)\) \(\chi_{4598}(509,\cdot)\) \(\chi_{4598}(515,\cdot)\) \(\chi_{4598}(553,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{495})$ |
| Fixed field: | Number field defined by a degree 990 polynomial (not computed) |
Values on generators
\((3269,3631)\) → \((e\left(\frac{38}{55}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 4598 }(383, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{338}{495}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{17}{45}\right)\) | \(e\left(\frac{389}{990}\right)\) | \(e\left(\frac{863}{990}\right)\) | \(e\left(\frac{38}{495}\right)\) | \(e\left(\frac{71}{198}\right)\) | \(e\left(\frac{80}{99}\right)\) | \(e\left(\frac{181}{495}\right)\) |