Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 179 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 89 |
| Real | = | no |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | yes |
| Minimal | = | yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
| Parity | = | even |
| Orbit label | = | 179.c |
| Orbit index | = | 3 |
Galois orbit
\(\chi_{179}(3,\cdot)\) \(\chi_{179}(4,\cdot)\) \(\chi_{179}(5,\cdot)\) \(\chi_{179}(9,\cdot)\) \(\chi_{179}(12,\cdot)\) \(\chi_{179}(13,\cdot)\) \(\chi_{179}(14,\cdot)\) \(\chi_{179}(15,\cdot)\) \(\chi_{179}(16,\cdot)\) \(\chi_{179}(17,\cdot)\) \(\chi_{179}(19,\cdot)\) \(\chi_{179}(20,\cdot)\) \(\chi_{179}(22,\cdot)\) \(\chi_{179}(25,\cdot)\) \(\chi_{179}(27,\cdot)\) \(\chi_{179}(29,\cdot)\) \(\chi_{179}(31,\cdot)\) \(\chi_{179}(36,\cdot)\) \(\chi_{179}(39,\cdot)\) \(\chi_{179}(42,\cdot)\) \(\chi_{179}(43,\cdot)\) \(\chi_{179}(45,\cdot)\) \(\chi_{179}(46,\cdot)\) \(\chi_{179}(47,\cdot)\) \(\chi_{179}(48,\cdot)\) \(\chi_{179}(49,\cdot)\) \(\chi_{179}(51,\cdot)\) \(\chi_{179}(52,\cdot)\) \(\chi_{179}(56,\cdot)\) \(\chi_{179}(57,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{18}{89}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{18}{89}\right)\) | \(e\left(\frac{75}{89}\right)\) | \(e\left(\frac{36}{89}\right)\) | \(e\left(\frac{81}{89}\right)\) | \(e\left(\frac{4}{89}\right)\) | \(e\left(\frac{52}{89}\right)\) | \(e\left(\frac{54}{89}\right)\) | \(e\left(\frac{61}{89}\right)\) | \(e\left(\frac{10}{89}\right)\) | \(e\left(\frac{3}{89}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{89})\) |