Basic properties
| Modulus: | \(4608\) | |
| Conductor: | \(256\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(64\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{256}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4608.bv
\(\chi_{4608}(55,\cdot)\) \(\chi_{4608}(199,\cdot)\) \(\chi_{4608}(343,\cdot)\) \(\chi_{4608}(487,\cdot)\) \(\chi_{4608}(631,\cdot)\) \(\chi_{4608}(775,\cdot)\) \(\chi_{4608}(919,\cdot)\) \(\chi_{4608}(1063,\cdot)\) \(\chi_{4608}(1207,\cdot)\) \(\chi_{4608}(1351,\cdot)\) \(\chi_{4608}(1495,\cdot)\) \(\chi_{4608}(1639,\cdot)\) \(\chi_{4608}(1783,\cdot)\) \(\chi_{4608}(1927,\cdot)\) \(\chi_{4608}(2071,\cdot)\) \(\chi_{4608}(2215,\cdot)\) \(\chi_{4608}(2359,\cdot)\) \(\chi_{4608}(2503,\cdot)\) \(\chi_{4608}(2647,\cdot)\) \(\chi_{4608}(2791,\cdot)\) \(\chi_{4608}(2935,\cdot)\) \(\chi_{4608}(3079,\cdot)\) \(\chi_{4608}(3223,\cdot)\) \(\chi_{4608}(3367,\cdot)\) \(\chi_{4608}(3511,\cdot)\) \(\chi_{4608}(3655,\cdot)\) \(\chi_{4608}(3799,\cdot)\) \(\chi_{4608}(3943,\cdot)\) \(\chi_{4608}(4087,\cdot)\) \(\chi_{4608}(4231,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((3583,2053,4097)\) → \((-1,e\left(\frac{23}{64}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4608 }(3223, a) \) | \(-1\) | \(1\) | \(e\left(\frac{23}{64}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{49}{64}\right)\) | \(e\left(\frac{17}{32}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{13}{64}\right)\) | \(e\left(\frac{3}{8}\right)\) |