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]
| ||
| Primitive | = | Yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
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| Parity | = | Even |
| Orbit label | = | 4033.ia |
| Orbit index | = | 209 |
Galois orbit
\(\chi_{4033}(13,\cdot)\) \(\chi_{4033}(204,\cdot)\) \(\chi_{4033}(257,\cdot)\) \(\chi_{4033}(383,\cdot)\) \(\chi_{4033}(392,\cdot)\) \(\chi_{4033}(426,\cdot)\) \(\chi_{4033}(505,\cdot)\) \(\chi_{4033}(575,\cdot)\) \(\chi_{4033}(930,\cdot)\) \(\chi_{4033}(1053,\cdot)\) \(\chi_{4033}(1142,\cdot)\) \(\chi_{4033}(1241,\cdot)\) \(\chi_{4033}(1297,\cdot)\) \(\chi_{4033}(1367,\cdot)\) \(\chi_{4033}(1411,\cdot)\) \(\chi_{4033}(1720,\cdot)\) \(\chi_{4033}(1791,\cdot)\) \(\chi_{4033}(1835,\cdot)\) \(\chi_{4033}(2198,\cdot)\) \(\chi_{4033}(2242,\cdot)\) \(\chi_{4033}(2313,\cdot)\) \(\chi_{4033}(2622,\cdot)\) \(\chi_{4033}(2666,\cdot)\) \(\chi_{4033}(2736,\cdot)\) \(\chi_{4033}(2792,\cdot)\) \(\chi_{4033}(2891,\cdot)\) \(\chi_{4033}(2980,\cdot)\) \(\chi_{4033}(3103,\cdot)\) \(\chi_{4033}(3458,\cdot)\) \(\chi_{4033}(3528,\cdot)\) ...
Values on generators
\((1963,2295)\) → \((e\left(\frac{11}{36}\right),e\left(\frac{67}{108}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{19}{108}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{16}{27}\right)\) | \(1\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{91}{108}\right)\) | \(e\left(\frac{71}{108}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{108})\) |