Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 4033 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 108 |
| Real | = | no |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
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| Primitive | = | yes |
| Minimal | = | yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
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| Parity | = | even |
| Orbit label | = | 4033.hy |
| Orbit index | = | 207 |
Galois orbit
\(\chi_{4033}(24,\cdot)\) \(\chi_{4033}(166,\cdot)\) \(\chi_{4033}(168,\cdot)\) \(\chi_{4033}(466,\cdot)\) \(\chi_{4033}(476,\cdot)\) \(\chi_{4033}(701,\cdot)\) \(\chi_{4033}(942,\cdot)\) \(\chi_{4033}(994,\cdot)\) \(\chi_{4033}(1108,\cdot)\) \(\chi_{4033}(1132,\cdot)\) \(\chi_{4033}(1162,\cdot)\) \(\chi_{4033}(1314,\cdot)\) \(\chi_{4033}(1364,\cdot)\) \(\chi_{4033}(1482,\cdot)\) \(\chi_{4033}(1537,\cdot)\) \(\chi_{4033}(1795,\cdot)\) \(\chi_{4033}(1863,\cdot)\) \(\chi_{4033}(1948,\cdot)\) \(\chi_{4033}(2085,\cdot)\) \(\chi_{4033}(2170,\cdot)\) \(\chi_{4033}(2238,\cdot)\) \(\chi_{4033}(2496,\cdot)\) \(\chi_{4033}(2551,\cdot)\) \(\chi_{4033}(2669,\cdot)\) \(\chi_{4033}(2719,\cdot)\) \(\chi_{4033}(2871,\cdot)\) \(\chi_{4033}(2901,\cdot)\) \(\chi_{4033}(2925,\cdot)\) \(\chi_{4033}(3039,\cdot)\) \(\chi_{4033}(3091,\cdot)\) ...
Values on generators
\((1963,2295)\) → \((e\left(\frac{5}{36}\right),e\left(\frac{31}{108}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(-1\) | \(e\left(\frac{29}{54}\right)\) | \(1\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(-1\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{55}{108}\right)\) | \(e\left(\frac{107}{108}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{108})\) |