Basic properties
| Modulus: | \(3584\) | |
| 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 \(\chi_{256}(235,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3584.bu
\(\chi_{3584}(71,\cdot)\) \(\chi_{3584}(183,\cdot)\) \(\chi_{3584}(295,\cdot)\) \(\chi_{3584}(407,\cdot)\) \(\chi_{3584}(519,\cdot)\) \(\chi_{3584}(631,\cdot)\) \(\chi_{3584}(743,\cdot)\) \(\chi_{3584}(855,\cdot)\) \(\chi_{3584}(967,\cdot)\) \(\chi_{3584}(1079,\cdot)\) \(\chi_{3584}(1191,\cdot)\) \(\chi_{3584}(1303,\cdot)\) \(\chi_{3584}(1415,\cdot)\) \(\chi_{3584}(1527,\cdot)\) \(\chi_{3584}(1639,\cdot)\) \(\chi_{3584}(1751,\cdot)\) \(\chi_{3584}(1863,\cdot)\) \(\chi_{3584}(1975,\cdot)\) \(\chi_{3584}(2087,\cdot)\) \(\chi_{3584}(2199,\cdot)\) \(\chi_{3584}(2311,\cdot)\) \(\chi_{3584}(2423,\cdot)\) \(\chi_{3584}(2535,\cdot)\) \(\chi_{3584}(2647,\cdot)\) \(\chi_{3584}(2759,\cdot)\) \(\chi_{3584}(2871,\cdot)\) \(\chi_{3584}(2983,\cdot)\) \(\chi_{3584}(3095,\cdot)\) \(\chi_{3584}(3207,\cdot)\) \(\chi_{3584}(3319,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1023,1541,1025)\) → \((-1,e\left(\frac{45}{64}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3584 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{64}\right)\) | \(e\left(\frac{45}{64}\right)\) | \(e\left(\frac{7}{32}\right)\) | \(e\left(\frac{17}{64}\right)\) | \(e\left(\frac{3}{64}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{43}{64}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{13}{32}\right)\) |