Basic properties
| Modulus: | \(4608\) | |
| Conductor: | \(512\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(128\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{512}(309,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4608.cb
\(\chi_{4608}(37,\cdot)\) \(\chi_{4608}(109,\cdot)\) \(\chi_{4608}(181,\cdot)\) \(\chi_{4608}(253,\cdot)\) \(\chi_{4608}(325,\cdot)\) \(\chi_{4608}(397,\cdot)\) \(\chi_{4608}(469,\cdot)\) \(\chi_{4608}(541,\cdot)\) \(\chi_{4608}(613,\cdot)\) \(\chi_{4608}(685,\cdot)\) \(\chi_{4608}(757,\cdot)\) \(\chi_{4608}(829,\cdot)\) \(\chi_{4608}(901,\cdot)\) \(\chi_{4608}(973,\cdot)\) \(\chi_{4608}(1045,\cdot)\) \(\chi_{4608}(1117,\cdot)\) \(\chi_{4608}(1189,\cdot)\) \(\chi_{4608}(1261,\cdot)\) \(\chi_{4608}(1333,\cdot)\) \(\chi_{4608}(1405,\cdot)\) \(\chi_{4608}(1477,\cdot)\) \(\chi_{4608}(1549,\cdot)\) \(\chi_{4608}(1621,\cdot)\) \(\chi_{4608}(1693,\cdot)\) \(\chi_{4608}(1765,\cdot)\) \(\chi_{4608}(1837,\cdot)\) \(\chi_{4608}(1909,\cdot)\) \(\chi_{4608}(1981,\cdot)\) \(\chi_{4608}(2053,\cdot)\) \(\chi_{4608}(2125,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{128})$ |
| Fixed field: | Number field defined by a degree 128 polynomial (not computed) |
Values on generators
\((3583,2053,4097)\) → \((1,e\left(\frac{69}{128}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 4608 }(1333, a) \) | \(1\) | \(1\) | \(e\left(\frac{69}{128}\right)\) | \(e\left(\frac{57}{64}\right)\) | \(e\left(\frac{105}{128}\right)\) | \(e\left(\frac{107}{128}\right)\) | \(e\left(\frac{3}{32}\right)\) | \(e\left(\frac{51}{128}\right)\) | \(e\left(\frac{35}{64}\right)\) | \(e\left(\frac{5}{64}\right)\) | \(e\left(\frac{39}{128}\right)\) | \(e\left(\frac{5}{16}\right)\) |