Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 4025 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 660 |
| 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 | = | 4025.do |
| Orbit index | = | 93 |
Galois orbit
\(\chi_{4025}(3,\cdot)\) \(\chi_{4025}(12,\cdot)\) \(\chi_{4025}(52,\cdot)\) \(\chi_{4025}(73,\cdot)\) \(\chi_{4025}(87,\cdot)\) \(\chi_{4025}(108,\cdot)\) \(\chi_{4025}(117,\cdot)\) \(\chi_{4025}(173,\cdot)\) \(\chi_{4025}(187,\cdot)\) \(\chi_{4025}(192,\cdot)\) \(\chi_{4025}(213,\cdot)\) \(\chi_{4025}(248,\cdot)\) \(\chi_{4025}(262,\cdot)\) \(\chi_{4025}(278,\cdot)\) \(\chi_{4025}(292,\cdot)\) \(\chi_{4025}(348,\cdot)\) \(\chi_{4025}(353,\cdot)\) \(\chi_{4025}(397,\cdot)\) \(\chi_{4025}(423,\cdot)\) \(\chi_{4025}(453,\cdot)\) \(\chi_{4025}(472,\cdot)\) \(\chi_{4025}(537,\cdot)\) \(\chi_{4025}(542,\cdot)\) \(\chi_{4025}(558,\cdot)\) \(\chi_{4025}(577,\cdot)\) \(\chi_{4025}(633,\cdot)\) \(\chi_{4025}(647,\cdot)\) \(\chi_{4025}(698,\cdot)\) \(\chi_{4025}(703,\cdot)\) \(\chi_{4025}(717,\cdot)\) ...
Values on generators
\((2577,1151,3501)\) → \((e\left(\frac{9}{20}\right),e\left(\frac{5}{6}\right),e\left(\frac{10}{11}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 6 | 8 | 9 | 11 | 12 | 13 | 16 |
| \(1\) | \(1\) | \(e\left(\frac{617}{660}\right)\) | \(e\left(\frac{349}{660}\right)\) | \(e\left(\frac{287}{330}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{177}{220}\right)\) | \(e\left(\frac{19}{330}\right)\) | \(e\left(\frac{118}{165}\right)\) | \(e\left(\frac{263}{660}\right)\) | \(e\left(\frac{171}{220}\right)\) | \(e\left(\frac{122}{165}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{660})\) |