Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 1000 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 100 |
| 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 | = | 1000.bj |
| Orbit index | = | 36 |
Galois orbit
\(\chi_{1000}(13,\cdot)\) \(\chi_{1000}(37,\cdot)\) \(\chi_{1000}(53,\cdot)\) \(\chi_{1000}(77,\cdot)\) \(\chi_{1000}(117,\cdot)\) \(\chi_{1000}(133,\cdot)\) \(\chi_{1000}(173,\cdot)\) \(\chi_{1000}(197,\cdot)\) \(\chi_{1000}(213,\cdot)\) \(\chi_{1000}(237,\cdot)\) \(\chi_{1000}(253,\cdot)\) \(\chi_{1000}(277,\cdot)\) \(\chi_{1000}(317,\cdot)\) \(\chi_{1000}(333,\cdot)\) \(\chi_{1000}(373,\cdot)\) \(\chi_{1000}(397,\cdot)\) \(\chi_{1000}(413,\cdot)\) \(\chi_{1000}(437,\cdot)\) \(\chi_{1000}(453,\cdot)\) \(\chi_{1000}(477,\cdot)\) \(\chi_{1000}(517,\cdot)\) \(\chi_{1000}(533,\cdot)\) \(\chi_{1000}(573,\cdot)\) \(\chi_{1000}(597,\cdot)\) \(\chi_{1000}(613,\cdot)\) \(\chi_{1000}(637,\cdot)\) \(\chi_{1000}(653,\cdot)\) \(\chi_{1000}(677,\cdot)\) \(\chi_{1000}(717,\cdot)\) \(\chi_{1000}(733,\cdot)\) ...
Values on generators
\((751,501,377)\) → \((1,-1,e\left(\frac{93}{100}\right))\)
Values
| -1 | 1 | 3 | 7 | 9 | 11 | 13 | 17 | 19 | 21 | 23 | 27 |
| \(-1\) | \(1\) | \(e\left(\frac{1}{100}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{9}{50}\right)\) | \(e\left(\frac{77}{100}\right)\) | \(e\left(\frac{89}{100}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{83}{100}\right)\) | \(e\left(\frac{3}{100}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{100})\) |