Basic properties
| Modulus: | \(36864\) | |
| Conductor: | \(4096\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1024\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4096}(685,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 36864.cz
\(\chi_{36864}(37,\cdot)\) \(\chi_{36864}(109,\cdot)\) \(\chi_{36864}(181,\cdot)\) \(\chi_{36864}(253,\cdot)\) \(\chi_{36864}(325,\cdot)\) \(\chi_{36864}(397,\cdot)\) \(\chi_{36864}(469,\cdot)\) \(\chi_{36864}(541,\cdot)\) \(\chi_{36864}(613,\cdot)\) \(\chi_{36864}(685,\cdot)\) \(\chi_{36864}(757,\cdot)\) \(\chi_{36864}(829,\cdot)\) \(\chi_{36864}(901,\cdot)\) \(\chi_{36864}(973,\cdot)\) \(\chi_{36864}(1045,\cdot)\) \(\chi_{36864}(1117,\cdot)\) \(\chi_{36864}(1189,\cdot)\) \(\chi_{36864}(1261,\cdot)\) \(\chi_{36864}(1333,\cdot)\) \(\chi_{36864}(1405,\cdot)\) \(\chi_{36864}(1477,\cdot)\) \(\chi_{36864}(1549,\cdot)\) \(\chi_{36864}(1621,\cdot)\) \(\chi_{36864}(1693,\cdot)\) \(\chi_{36864}(1765,\cdot)\) \(\chi_{36864}(1837,\cdot)\) \(\chi_{36864}(1909,\cdot)\) \(\chi_{36864}(1981,\cdot)\) \(\chi_{36864}(2053,\cdot)\) \(\chi_{36864}(2125,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1024})$ |
| Fixed field: | Number field defined by a degree 1024 polynomial (not computed) |
Values on generators
\((8191,20485,4097)\) → \((1,e\left(\frac{551}{1024}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 36864 }(685, a) \) | \(1\) | \(1\) | \(e\left(\frac{551}{1024}\right)\) | \(e\left(\frac{99}{512}\right)\) | \(e\left(\frac{627}{1024}\right)\) | \(e\left(\frac{873}{1024}\right)\) | \(e\left(\frac{177}{256}\right)\) | \(e\left(\frac{513}{1024}\right)\) | \(e\left(\frac{209}{512}\right)\) | \(e\left(\frac{39}{512}\right)\) | \(e\left(\frac{445}{1024}\right)\) | \(e\left(\frac{119}{128}\right)\) |