Basic properties
| Modulus: | \(4598\) | |
| Conductor: | \(2299\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(330\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2299}(1323,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4598.bq
\(\chi_{4598}(31,\cdot)\) \(\chi_{4598}(69,\cdot)\) \(\chi_{4598}(103,\cdot)\) \(\chi_{4598}(141,\cdot)\) \(\chi_{4598}(179,\cdot)\) \(\chi_{4598}(335,\cdot)\) \(\chi_{4598}(411,\cdot)\) \(\chi_{4598}(445,\cdot)\) \(\chi_{4598}(449,\cdot)\) \(\chi_{4598}(521,\cdot)\) \(\chi_{4598}(559,\cdot)\) \(\chi_{4598}(597,\cdot)\) \(\chi_{4598}(829,\cdot)\) \(\chi_{4598}(863,\cdot)\) \(\chi_{4598}(867,\cdot)\) \(\chi_{4598}(905,\cdot)\) \(\chi_{4598}(939,\cdot)\) \(\chi_{4598}(1015,\cdot)\) \(\chi_{4598}(1171,\cdot)\) \(\chi_{4598}(1247,\cdot)\) \(\chi_{4598}(1281,\cdot)\) \(\chi_{4598}(1285,\cdot)\) \(\chi_{4598}(1323,\cdot)\) \(\chi_{4598}(1357,\cdot)\) \(\chi_{4598}(1395,\cdot)\) \(\chi_{4598}(1433,\cdot)\) \(\chi_{4598}(1589,\cdot)\) \(\chi_{4598}(1665,\cdot)\) \(\chi_{4598}(1699,\cdot)\) \(\chi_{4598}(1741,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{165})$ |
| Fixed field: | Number field defined by a degree 330 polynomial (not computed) |
Values on generators
\((3269,3631)\) → \((e\left(\frac{29}{55}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 4598 }(1323, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{58}{165}\right)\) | \(e\left(\frac{38}{55}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{139}{330}\right)\) | \(e\left(\frac{193}{330}\right)\) | \(e\left(\frac{28}{165}\right)\) | \(e\left(\frac{61}{66}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{116}{165}\right)\) |