Basic properties
| Modulus: | \(4608\) | |
| Conductor: | \(1152\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(96\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1152}(803,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4608.bw
\(\chi_{4608}(47,\cdot)\) \(\chi_{4608}(239,\cdot)\) \(\chi_{4608}(335,\cdot)\) \(\chi_{4608}(527,\cdot)\) \(\chi_{4608}(623,\cdot)\) \(\chi_{4608}(815,\cdot)\) \(\chi_{4608}(911,\cdot)\) \(\chi_{4608}(1103,\cdot)\) \(\chi_{4608}(1199,\cdot)\) \(\chi_{4608}(1391,\cdot)\) \(\chi_{4608}(1487,\cdot)\) \(\chi_{4608}(1679,\cdot)\) \(\chi_{4608}(1775,\cdot)\) \(\chi_{4608}(1967,\cdot)\) \(\chi_{4608}(2063,\cdot)\) \(\chi_{4608}(2255,\cdot)\) \(\chi_{4608}(2351,\cdot)\) \(\chi_{4608}(2543,\cdot)\) \(\chi_{4608}(2639,\cdot)\) \(\chi_{4608}(2831,\cdot)\) \(\chi_{4608}(2927,\cdot)\) \(\chi_{4608}(3119,\cdot)\) \(\chi_{4608}(3215,\cdot)\) \(\chi_{4608}(3407,\cdot)\) \(\chi_{4608}(3503,\cdot)\) \(\chi_{4608}(3695,\cdot)\) \(\chi_{4608}(3791,\cdot)\) \(\chi_{4608}(3983,\cdot)\) \(\chi_{4608}(4079,\cdot)\) \(\chi_{4608}(4271,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{96})$ |
| Fixed field: | Number field defined by a degree 96 polynomial |
Values on generators
\((3583,2053,4097)\) → \((-1,e\left(\frac{11}{32}\right),e\left(\frac{1}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4608 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{96}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{85}{96}\right)\) | \(e\left(\frac{47}{96}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{13}{32}\right)\) | \(e\left(\frac{7}{48}\right)\) | \(e\left(\frac{17}{48}\right)\) | \(e\left(\frac{43}{96}\right)\) | \(e\left(\frac{7}{12}\right)\) |