Basic properties
| Modulus: | \(4864\) | |
| Conductor: | \(2432\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2432}(501,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4864.co
\(\chi_{4864}(121,\cdot)\) \(\chi_{4864}(201,\cdot)\) \(\chi_{4864}(425,\cdot)\) \(\chi_{4864}(505,\cdot)\) \(\chi_{4864}(729,\cdot)\) \(\chi_{4864}(809,\cdot)\) \(\chi_{4864}(1033,\cdot)\) \(\chi_{4864}(1113,\cdot)\) \(\chi_{4864}(1337,\cdot)\) \(\chi_{4864}(1417,\cdot)\) \(\chi_{4864}(1641,\cdot)\) \(\chi_{4864}(1721,\cdot)\) \(\chi_{4864}(1945,\cdot)\) \(\chi_{4864}(2025,\cdot)\) \(\chi_{4864}(2249,\cdot)\) \(\chi_{4864}(2329,\cdot)\) \(\chi_{4864}(2553,\cdot)\) \(\chi_{4864}(2633,\cdot)\) \(\chi_{4864}(2857,\cdot)\) \(\chi_{4864}(2937,\cdot)\) \(\chi_{4864}(3161,\cdot)\) \(\chi_{4864}(3241,\cdot)\) \(\chi_{4864}(3465,\cdot)\) \(\chi_{4864}(3545,\cdot)\) \(\chi_{4864}(3769,\cdot)\) \(\chi_{4864}(3849,\cdot)\) \(\chi_{4864}(4073,\cdot)\) \(\chi_{4864}(4153,\cdot)\) \(\chi_{4864}(4377,\cdot)\) \(\chi_{4864}(4457,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((3839,2053,4353)\) → \((1,e\left(\frac{21}{32}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
| \( \chi_{ 4864 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{96}\right)\) | \(e\left(\frac{95}{96}\right)\) | \(e\left(\frac{9}{16}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{25}{32}\right)\) | \(e\left(\frac{49}{96}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{83}{96}\right)\) | \(e\left(\frac{41}{48}\right)\) |