Basic properties
sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Conductor | = | 199 |
sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Order | = | 99 |
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 | = | 199.k |
Orbit index | = | 11 |
Galois orbit
\(\chi_{199}(2,\cdot)\) \(\chi_{199}(4,\cdot)\) \(\chi_{199}(7,\cdot)\) \(\chi_{199}(9,\cdot)\) \(\chi_{199}(10,\cdot)\) \(\chi_{199}(13,\cdot)\) \(\chi_{199}(14,\cdot)\) \(\chi_{199}(16,\cdot)\) \(\chi_{199}(20,\cdot)\) \(\chi_{199}(23,\cdot)\) \(\chi_{199}(26,\cdot)\) \(\chi_{199}(29,\cdot)\) \(\chi_{199}(31,\cdot)\) \(\chi_{199}(32,\cdot)\) \(\chi_{199}(33,\cdot)\) \(\chi_{199}(35,\cdot)\) \(\chi_{199}(36,\cdot)\) \(\chi_{199}(45,\cdot)\) \(\chi_{199}(46,\cdot)\) \(\chi_{199}(47,\cdot)\) \(\chi_{199}(49,\cdot)\) \(\chi_{199}(50,\cdot)\) \(\chi_{199}(51,\cdot)\) \(\chi_{199}(53,\cdot)\) \(\chi_{199}(56,\cdot)\) \(\chi_{199}(57,\cdot)\) \(\chi_{199}(65,\cdot)\) \(\chi_{199}(66,\cdot)\) \(\chi_{199}(70,\cdot)\) \(\chi_{199}(72,\cdot)\) ...
Values on generators
\(3\) → \(e\left(\frac{1}{99}\right)\)
Values
-1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
\(1\) | \(1\) | \(e\left(\frac{7}{99}\right)\) | \(e\left(\frac{1}{99}\right)\) | \(e\left(\frac{14}{99}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{8}{99}\right)\) | \(e\left(\frac{43}{99}\right)\) | \(e\left(\frac{7}{33}\right)\) | \(e\left(\frac{2}{99}\right)\) | \(e\left(\frac{46}{99}\right)\) | \(e\left(\frac{10}{11}\right)\) |
Related number fields
Field of values | \(\Q(\zeta_{99})\) |