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 |
| Minimal | = | yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
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| Parity | = | even |
| Orbit label | = | 4025.dl |
| Orbit index | = | 90 |
Galois orbit
\(\chi_{4025}(19,\cdot)\) \(\chi_{4025}(89,\cdot)\) \(\chi_{4025}(129,\cdot)\) \(\chi_{4025}(159,\cdot)\) \(\chi_{4025}(194,\cdot)\) \(\chi_{4025}(264,\cdot)\) \(\chi_{4025}(304,\cdot)\) \(\chi_{4025}(339,\cdot)\) \(\chi_{4025}(444,\cdot)\) \(\chi_{4025}(479,\cdot)\) \(\chi_{4025}(544,\cdot)\) \(\chi_{4025}(619,\cdot)\) \(\chi_{4025}(654,\cdot)\) \(\chi_{4025}(684,\cdot)\) \(\chi_{4025}(789,\cdot)\) \(\chi_{4025}(894,\cdot)\) \(\chi_{4025}(934,\cdot)\) \(\chi_{4025}(964,\cdot)\) \(\chi_{4025}(1004,\cdot)\) \(\chi_{4025}(1069,\cdot)\) \(\chi_{4025}(1109,\cdot)\) \(\chi_{4025}(1144,\cdot)\) \(\chi_{4025}(1279,\cdot)\) \(\chi_{4025}(1284,\cdot)\) \(\chi_{4025}(1354,\cdot)\) \(\chi_{4025}(1454,\cdot)\) \(\chi_{4025}(1459,\cdot)\) \(\chi_{4025}(1489,\cdot)\) \(\chi_{4025}(1529,\cdot)\) \(\chi_{4025}(1594,\cdot)\) ...
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{5}{6}\right),e\left(\frac{15}{22}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 6 | 8 | 9 | 11 | 12 | 13 | 16 |
| \(1\) | \(1\) | \(e\left(\frac{307}{330}\right)\) | \(e\left(\frac{7}{165}\right)\) | \(e\left(\frac{142}{165}\right)\) | \(e\left(\frac{107}{110}\right)\) | \(e\left(\frac{87}{110}\right)\) | \(e\left(\frac{14}{165}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{149}{165}\right)\) | \(e\left(\frac{8}{55}\right)\) | \(e\left(\frac{119}{165}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{165})\) |