Basic properties
| Modulus: | \(24704\) | |
| Conductor: | \(3088\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3088}(2347,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 24704.pu
\(\chi_{24704}(31,\cdot)\) \(\chi_{24704}(479,\cdot)\) \(\chi_{24704}(1183,\cdot)\) \(\chi_{24704}(1823,\cdot)\) \(\chi_{24704}(3935,\cdot)\) \(\chi_{24704}(4831,\cdot)\) \(\chi_{24704}(5855,\cdot)\) \(\chi_{24704}(6111,\cdot)\) \(\chi_{24704}(7135,\cdot)\) \(\chi_{24704}(8031,\cdot)\) \(\chi_{24704}(10143,\cdot)\) \(\chi_{24704}(10783,\cdot)\) \(\chi_{24704}(11487,\cdot)\) \(\chi_{24704}(11935,\cdot)\) \(\chi_{24704}(12191,\cdot)\) \(\chi_{24704}(12255,\cdot)\) \(\chi_{24704}(12447,\cdot)\) \(\chi_{24704}(13023,\cdot)\) \(\chi_{24704}(14751,\cdot)\) \(\chi_{24704}(14879,\cdot)\) \(\chi_{24704}(16351,\cdot)\) \(\chi_{24704}(16735,\cdot)\) \(\chi_{24704}(17951,\cdot)\) \(\chi_{24704}(18719,\cdot)\) \(\chi_{24704}(19935,\cdot)\) \(\chi_{24704}(20319,\cdot)\) \(\chi_{24704}(21791,\cdot)\) \(\chi_{24704}(21919,\cdot)\) \(\chi_{24704}(23647,\cdot)\) \(\chi_{24704}(24223,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((24319,773,23937)\) → \((-1,i,e\left(\frac{41}{96}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 24704 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{65}{96}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(i\) | \(e\left(\frac{29}{32}\right)\) | \(e\left(\frac{31}{32}\right)\) | \(e\left(\frac{77}{96}\right)\) | \(e\left(\frac{23}{96}\right)\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{13}{24}\right)\) |