Basic properties
| Modulus: | \(4864\) | |
| Conductor: | \(4864\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(576\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4864.dd
\(\chi_{4864}(3,\cdot)\) \(\chi_{4864}(51,\cdot)\) \(\chi_{4864}(59,\cdot)\) \(\chi_{4864}(67,\cdot)\) \(\chi_{4864}(91,\cdot)\) \(\chi_{4864}(147,\cdot)\) \(\chi_{4864}(155,\cdot)\) \(\chi_{4864}(203,\cdot)\) \(\chi_{4864}(211,\cdot)\) \(\chi_{4864}(219,\cdot)\) \(\chi_{4864}(243,\cdot)\) \(\chi_{4864}(299,\cdot)\) \(\chi_{4864}(307,\cdot)\) \(\chi_{4864}(355,\cdot)\) \(\chi_{4864}(363,\cdot)\) \(\chi_{4864}(371,\cdot)\) \(\chi_{4864}(395,\cdot)\) \(\chi_{4864}(451,\cdot)\) \(\chi_{4864}(459,\cdot)\) \(\chi_{4864}(507,\cdot)\) \(\chi_{4864}(515,\cdot)\) \(\chi_{4864}(523,\cdot)\) \(\chi_{4864}(547,\cdot)\) \(\chi_{4864}(603,\cdot)\) \(\chi_{4864}(611,\cdot)\) \(\chi_{4864}(659,\cdot)\) \(\chi_{4864}(667,\cdot)\) \(\chi_{4864}(675,\cdot)\) \(\chi_{4864}(699,\cdot)\) \(\chi_{4864}(755,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{576})$ |
| Fixed field: | Number field defined by a degree 576 polynomial (not computed) |
Values on generators
\((3839,2053,4353)\) → \((-1,e\left(\frac{35}{64}\right),e\left(\frac{13}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4864 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{576}\right)\) | \(e\left(\frac{59}{576}\right)\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{17}{288}\right)\) | \(e\left(\frac{125}{192}\right)\) | \(e\left(\frac{181}{576}\right)\) | \(e\left(\frac{19}{144}\right)\) | \(e\left(\frac{77}{144}\right)\) | \(e\left(\frac{191}{576}\right)\) | \(e\left(\frac{173}{288}\right)\) |