Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 8041 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 560 |
| 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)
| ||
| Parity | = | Even |
| Orbit label | = | 8041.ft |
| Orbit index | = | 150 |
Galois orbit
\(\chi_{8041}(27,\cdot)\) \(\chi_{8041}(75,\cdot)\) \(\chi_{8041}(82,\cdot)\) \(\chi_{8041}(108,\cdot)\) \(\chi_{8041}(113,\cdot)\) \(\chi_{8041}(125,\cdot)\) \(\chi_{8041}(180,\cdot)\) \(\chi_{8041}(328,\cdot)\) \(\chi_{8041}(333,\cdot)\) \(\chi_{8041}(346,\cdot)\) \(\chi_{8041}(432,\cdot)\) \(\chi_{8041}(500,\cdot)\) \(\chi_{8041}(555,\cdot)\) \(\chi_{8041}(581,\cdot)\) \(\chi_{8041}(598,\cdot)\) \(\chi_{8041}(641,\cdot)\) \(\chi_{8041}(653,\cdot)\) \(\chi_{8041}(720,\cdot)\) \(\chi_{8041}(753,\cdot)\) \(\chi_{8041}(796,\cdot)\) \(\chi_{8041}(806,\cdot)\) \(\chi_{8041}(819,\cdot)\) \(\chi_{8041}(839,\cdot)\) \(\chi_{8041}(856,\cdot)\) \(\chi_{8041}(862,\cdot)\) \(\chi_{8041}(911,\cdot)\) \(\chi_{8041}(1059,\cdot)\) \(\chi_{8041}(1083,\cdot)\) \(\chi_{8041}(1193,\cdot)\) \(\chi_{8041}(1236,\cdot)\) ...
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{3}{16}\right),e\left(\frac{1}{14}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 |
| \(1\) | \(1\) | \(e\left(\frac{267}{280}\right)\) | \(e\left(\frac{257}{560}\right)\) | \(e\left(\frac{127}{140}\right)\) | \(e\left(\frac{181}{560}\right)\) | \(e\left(\frac{33}{80}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{241}{280}\right)\) | \(e\left(\frac{257}{280}\right)\) | \(e\left(\frac{31}{112}\right)\) | \(e\left(\frac{41}{112}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{560})\) |