Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 8041 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 56 |
| Real | = | No |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
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| Primitive | = | Yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
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| Parity | = | Even |
| Orbit label | = | 8041.dh |
| Orbit index | = | 86 |
Galois orbit
\(\chi_{8041}(32,\cdot)\) \(\chi_{8041}(604,\cdot)\) \(\chi_{8041}(978,\cdot)\) \(\chi_{8041}(1011,\cdot)\) \(\chi_{8041}(1341,\cdot)\) \(\chi_{8041}(1759,\cdot)\) \(\chi_{8041}(1957,\cdot)\) \(\chi_{8041}(2287,\cdot)\) \(\chi_{8041}(2650,\cdot)\) \(\chi_{8041}(2705,\cdot)\) \(\chi_{8041}(3442,\cdot)\) \(\chi_{8041}(3596,\cdot)\) \(\chi_{8041}(3816,\cdot)\) \(\chi_{8041}(4388,\cdot)\) \(\chi_{8041}(4762,\cdot)\) \(\chi_{8041}(5125,\cdot)\) \(\chi_{8041}(5268,\cdot)\) \(\chi_{8041}(6016,\cdot)\) \(\chi_{8041}(6071,\cdot)\) \(\chi_{8041}(6214,\cdot)\) \(\chi_{8041}(6434,\cdot)\) \(\chi_{8041}(6962,\cdot)\) \(\chi_{8041}(7380,\cdot)\) \(\chi_{8041}(7699,\cdot)\)
Values on generators
\((6580,2366,562)\) → \((-1,e\left(\frac{3}{8}\right),e\left(\frac{3}{14}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 12 |
| \(1\) | \(1\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{1}{14}\right)\) | \(e\left(\frac{13}{56}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{1}{8}\right)\) | \(e\left(\frac{17}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) | \(e\left(\frac{43}{56}\right)\) | \(e\left(\frac{37}{56}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{56})\) |