Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 4000 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 200 |
| Real | = | No |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | Yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
| Parity | = | Odd |
| Orbit label | = | 4000.cz |
| Orbit index | = | 78 |
Galois orbit
\(\chi_{4000}(53,\cdot)\) \(\chi_{4000}(77,\cdot)\) \(\chi_{4000}(133,\cdot)\) \(\chi_{4000}(213,\cdot)\) \(\chi_{4000}(237,\cdot)\) \(\chi_{4000}(317,\cdot)\) \(\chi_{4000}(373,\cdot)\) \(\chi_{4000}(397,\cdot)\) \(\chi_{4000}(453,\cdot)\) \(\chi_{4000}(477,\cdot)\) \(\chi_{4000}(533,\cdot)\) \(\chi_{4000}(613,\cdot)\) \(\chi_{4000}(637,\cdot)\) \(\chi_{4000}(717,\cdot)\) \(\chi_{4000}(773,\cdot)\) \(\chi_{4000}(797,\cdot)\) \(\chi_{4000}(853,\cdot)\) \(\chi_{4000}(877,\cdot)\) \(\chi_{4000}(933,\cdot)\) \(\chi_{4000}(1013,\cdot)\) \(\chi_{4000}(1037,\cdot)\) \(\chi_{4000}(1117,\cdot)\) \(\chi_{4000}(1173,\cdot)\) \(\chi_{4000}(1197,\cdot)\) \(\chi_{4000}(1253,\cdot)\) \(\chi_{4000}(1277,\cdot)\) \(\chi_{4000}(1333,\cdot)\) \(\chi_{4000}(1413,\cdot)\) \(\chi_{4000}(1437,\cdot)\) \(\chi_{4000}(1517,\cdot)\) ...
Values on generators
\((2751,2501,1377)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{33}{100}\right))\)
Values
| -1 | 1 | 3 | 7 | 9 | 11 | 13 | 17 | 19 | 21 | 23 | 27 |
| \(-1\) | \(1\) | \(e\left(\frac{187}{200}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{87}{100}\right)\) | \(e\left(\frac{91}{200}\right)\) | \(e\left(\frac{199}{200}\right)\) | \(e\left(\frac{59}{100}\right)\) | \(e\left(\frac{13}{200}\right)\) | \(e\left(\frac{147}{200}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{161}{200}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{200})\) |