Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 4025 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 330 |
| 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)
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| Parity | = | Odd |
| Orbit label | = | 4025.di |
| Orbit index | = | 87 |
Galois orbit
\(\chi_{4025}(31,\cdot)\) \(\chi_{4025}(96,\cdot)\) \(\chi_{4025}(131,\cdot)\) \(\chi_{4025}(236,\cdot)\) \(\chi_{4025}(271,\cdot)\) \(\chi_{4025}(311,\cdot)\) \(\chi_{4025}(381,\cdot)\) \(\chi_{4025}(416,\cdot)\) \(\chi_{4025}(446,\cdot)\) \(\chi_{4025}(486,\cdot)\) \(\chi_{4025}(556,\cdot)\) \(\chi_{4025}(591,\cdot)\) \(\chi_{4025}(656,\cdot)\) \(\chi_{4025}(696,\cdot)\) \(\chi_{4025}(731,\cdot)\) \(\chi_{4025}(761,\cdot)\) \(\chi_{4025}(831,\cdot)\) \(\chi_{4025}(836,\cdot)\) \(\chi_{4025}(906,\cdot)\) \(\chi_{4025}(936,\cdot)\) \(\chi_{4025}(1041,\cdot)\) \(\chi_{4025}(1116,\cdot)\) \(\chi_{4025}(1181,\cdot)\) \(\chi_{4025}(1186,\cdot)\) \(\chi_{4025}(1221,\cdot)\) \(\chi_{4025}(1291,\cdot)\) \(\chi_{4025}(1361,\cdot)\) \(\chi_{4025}(1396,\cdot)\) \(\chi_{4025}(1461,\cdot)\) \(\chi_{4025}(1531,\cdot)\) ...
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{1}{6}\right),e\left(\frac{3}{11}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 6 | 8 | 9 | 11 | 12 | 13 | 16 |
| \(-1\) | \(1\) | \(e\left(\frac{46}{165}\right)\) | \(e\left(\frac{109}{330}\right)\) | \(e\left(\frac{92}{165}\right)\) | \(e\left(\frac{67}{110}\right)\) | \(e\left(\frac{46}{55}\right)\) | \(e\left(\frac{109}{165}\right)\) | \(e\left(\frac{86}{165}\right)\) | \(e\left(\frac{293}{330}\right)\) | \(e\left(\frac{101}{110}\right)\) | \(e\left(\frac{19}{165}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{165})\) |