Basic properties
sage: chi.conductor()
pari: znconreyconductor(g,chi)
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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]
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Primitive | = | Yes |
sage: chi.is_odd()
pari: zncharisodd(g,chi)
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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 | \(\Q(\zeta_{89})\) |