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 \(\chi_{256}(85,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3584.bs
\(\chi_{3584}(57,\cdot)\) \(\chi_{3584}(169,\cdot)\) \(\chi_{3584}(281,\cdot)\) \(\chi_{3584}(393,\cdot)\) \(\chi_{3584}(505,\cdot)\) \(\chi_{3584}(617,\cdot)\) \(\chi_{3584}(729,\cdot)\) \(\chi_{3584}(841,\cdot)\) \(\chi_{3584}(953,\cdot)\) \(\chi_{3584}(1065,\cdot)\) \(\chi_{3584}(1177,\cdot)\) \(\chi_{3584}(1289,\cdot)\) \(\chi_{3584}(1401,\cdot)\) \(\chi_{3584}(1513,\cdot)\) \(\chi_{3584}(1625,\cdot)\) \(\chi_{3584}(1737,\cdot)\) \(\chi_{3584}(1849,\cdot)\) \(\chi_{3584}(1961,\cdot)\) \(\chi_{3584}(2073,\cdot)\) \(\chi_{3584}(2185,\cdot)\) \(\chi_{3584}(2297,\cdot)\) \(\chi_{3584}(2409,\cdot)\) \(\chi_{3584}(2521,\cdot)\) \(\chi_{3584}(2633,\cdot)\) \(\chi_{3584}(2745,\cdot)\) \(\chi_{3584}(2857,\cdot)\) \(\chi_{3584}(2969,\cdot)\) \(\chi_{3584}(3081,\cdot)\) \(\chi_{3584}(3193,\cdot)\) \(\chi_{3584}(3305,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{64})$ |
| Fixed field: | Number field defined by a degree 64 polynomial |
Values on generators
\((1023,1541,1025)\) → \((1,e\left(\frac{29}{64}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 3584 }(57, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{64}\right)\) | \(e\left(\frac{29}{64}\right)\) | \(e\left(\frac{23}{32}\right)\) | \(e\left(\frac{33}{64}\right)\) | \(e\left(\frac{19}{64}\right)\) | \(e\left(\frac{5}{16}\right)\) | \(e\left(\frac{11}{16}\right)\) | \(e\left(\frac{27}{64}\right)\) | \(e\left(\frac{11}{32}\right)\) | \(e\left(\frac{29}{32}\right)\) |