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 \(\chi_{2299}(299,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4598.bu
\(\chi_{4598}(13,\cdot)\) \(\chi_{4598}(29,\cdot)\) \(\chi_{4598}(41,\cdot)\) \(\chi_{4598}(51,\cdot)\) \(\chi_{4598}(79,\cdot)\) \(\chi_{4598}(105,\cdot)\) \(\chi_{4598}(117,\cdot)\) \(\chi_{4598}(127,\cdot)\) \(\chi_{4598}(129,\cdot)\) \(\chi_{4598}(167,\cdot)\) \(\chi_{4598}(173,\cdot)\) \(\chi_{4598}(193,\cdot)\) \(\chi_{4598}(205,\cdot)\) \(\chi_{4598}(211,\cdot)\) \(\chi_{4598}(249,\cdot)\) \(\chi_{4598}(261,\cdot)\) \(\chi_{4598}(281,\cdot)\) \(\chi_{4598}(299,\cdot)\) \(\chi_{4598}(325,\cdot)\) \(\chi_{4598}(337,\cdot)\) \(\chi_{4598}(371,\cdot)\) \(\chi_{4598}(393,\cdot)\) \(\chi_{4598}(409,\cdot)\) \(\chi_{4598}(413,\cdot)\) \(\chi_{4598}(431,\cdot)\) \(\chi_{4598}(447,\cdot)\) \(\chi_{4598}(459,\cdot)\) \(\chi_{4598}(469,\cdot)\) \(\chi_{4598}(497,\cdot)\) \(\chi_{4598}(523,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{495})$ |
| Fixed field: | Number field defined by a degree 990 polynomial (not computed) |
Values on generators
\((3269,3631)\) → \((e\left(\frac{61}{110}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 4598 }(299, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{90}\right)\) | \(e\left(\frac{128}{495}\right)\) | \(e\left(\frac{71}{330}\right)\) | \(e\left(\frac{32}{45}\right)\) | \(e\left(\frac{472}{495}\right)\) | \(e\left(\frac{113}{990}\right)\) | \(e\left(\frac{61}{990}\right)\) | \(e\left(\frac{7}{99}\right)\) | \(e\left(\frac{59}{99}\right)\) | \(e\left(\frac{256}{495}\right)\) |