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.ih |
| Orbit index | = | 216 |
Galois orbit
\(\chi_{4033}(14,\cdot)\) \(\chi_{4033}(51,\cdot)\) \(\chi_{4033}(162,\cdot)\) \(\chi_{4033}(208,\cdot)\) \(\chi_{4033}(288,\cdot)\) \(\chi_{4033}(430,\cdot)\) \(\chi_{4033}(473,\cdot)\) \(\chi_{4033}(532,\cdot)\) \(\chi_{4033}(822,\cdot)\) \(\chi_{4033}(1028,\cdot)\) \(\chi_{4033}(1050,\cdot)\) \(\chi_{4033}(1155,\cdot)\) \(\chi_{4033}(1266,\cdot)\) \(\chi_{4033}(1435,\cdot)\) \(\chi_{4033}(1842,\cdot)\) \(\chi_{4033}(1910,\cdot)\) \(\chi_{4033}(1932,\cdot)\) \(\chi_{4033}(1938,\cdot)\) \(\chi_{4033}(2095,\cdot)\) \(\chi_{4033}(2101,\cdot)\) \(\chi_{4033}(2123,\cdot)\) \(\chi_{4033}(2191,\cdot)\) \(\chi_{4033}(2598,\cdot)\) \(\chi_{4033}(2767,\cdot)\) \(\chi_{4033}(2878,\cdot)\) \(\chi_{4033}(2983,\cdot)\) \(\chi_{4033}(3005,\cdot)\) \(\chi_{4033}(3211,\cdot)\) \(\chi_{4033}(3501,\cdot)\) \(\chi_{4033}(3560,\cdot)\) ...
Values on generators
\((1963,2295)\) → \((e\left(\frac{11}{12}\right),e\left(\frac{37}{108}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{8}{27}\right)\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{101}{108}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{108})\) |