Basic properties
| Modulus: | \(4800\) | |
| Conductor: | \(1600\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1600}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4800.fj
\(\chi_{4800}(61,\cdot)\) \(\chi_{4800}(181,\cdot)\) \(\chi_{4800}(421,\cdot)\) \(\chi_{4800}(541,\cdot)\) \(\chi_{4800}(661,\cdot)\) \(\chi_{4800}(781,\cdot)\) \(\chi_{4800}(1021,\cdot)\) \(\chi_{4800}(1141,\cdot)\) \(\chi_{4800}(1261,\cdot)\) \(\chi_{4800}(1381,\cdot)\) \(\chi_{4800}(1621,\cdot)\) \(\chi_{4800}(1741,\cdot)\) \(\chi_{4800}(1861,\cdot)\) \(\chi_{4800}(1981,\cdot)\) \(\chi_{4800}(2221,\cdot)\) \(\chi_{4800}(2341,\cdot)\) \(\chi_{4800}(2461,\cdot)\) \(\chi_{4800}(2581,\cdot)\) \(\chi_{4800}(2821,\cdot)\) \(\chi_{4800}(2941,\cdot)\) \(\chi_{4800}(3061,\cdot)\) \(\chi_{4800}(3181,\cdot)\) \(\chi_{4800}(3421,\cdot)\) \(\chi_{4800}(3541,\cdot)\) \(\chi_{4800}(3661,\cdot)\) \(\chi_{4800}(3781,\cdot)\) \(\chi_{4800}(4021,\cdot)\) \(\chi_{4800}(4141,\cdot)\) \(\chi_{4800}(4261,\cdot)\) \(\chi_{4800}(4381,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{80})$ |
| Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((4351,901,1601,577)\) → \((1,e\left(\frac{3}{16}\right),1,e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 4800 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{1}{80}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{57}{80}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{53}{80}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{71}{80}\right)\) | \(e\left(\frac{33}{40}\right)\) |