Basic properties
| Modulus: | \(4864\) | |
| Conductor: | \(2432\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(288\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2432}(1515,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4864.cz
\(\chi_{4864}(71,\cdot)\) \(\chi_{4864}(135,\cdot)\) \(\chi_{4864}(167,\cdot)\) \(\chi_{4864}(231,\cdot)\) \(\chi_{4864}(279,\cdot)\) \(\chi_{4864}(295,\cdot)\) \(\chi_{4864}(375,\cdot)\) \(\chi_{4864}(439,\cdot)\) \(\chi_{4864}(471,\cdot)\) \(\chi_{4864}(535,\cdot)\) \(\chi_{4864}(583,\cdot)\) \(\chi_{4864}(599,\cdot)\) \(\chi_{4864}(679,\cdot)\) \(\chi_{4864}(743,\cdot)\) \(\chi_{4864}(775,\cdot)\) \(\chi_{4864}(839,\cdot)\) \(\chi_{4864}(887,\cdot)\) \(\chi_{4864}(903,\cdot)\) \(\chi_{4864}(983,\cdot)\) \(\chi_{4864}(1047,\cdot)\) \(\chi_{4864}(1079,\cdot)\) \(\chi_{4864}(1143,\cdot)\) \(\chi_{4864}(1191,\cdot)\) \(\chi_{4864}(1207,\cdot)\) \(\chi_{4864}(1287,\cdot)\) \(\chi_{4864}(1351,\cdot)\) \(\chi_{4864}(1383,\cdot)\) \(\chi_{4864}(1447,\cdot)\) \(\chi_{4864}(1495,\cdot)\) \(\chi_{4864}(1511,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{288})$ |
| Fixed field: | Number field defined by a degree 288 polynomial (not computed) |
Values on generators
\((3839,2053,4353)\) → \((-1,e\left(\frac{13}{32}\right),e\left(\frac{7}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4864 }(71, a) \) | \(1\) | \(1\) | \(e\left(\frac{223}{288}\right)\) | \(e\left(\frac{181}{288}\right)\) | \(e\left(\frac{43}{48}\right)\) | \(e\left(\frac{79}{144}\right)\) | \(e\left(\frac{67}{96}\right)\) | \(e\left(\frac{11}{288}\right)\) | \(e\left(\frac{29}{72}\right)\) | \(e\left(\frac{19}{72}\right)\) | \(e\left(\frac{193}{288}\right)\) | \(e\left(\frac{139}{144}\right)\) |