Basic properties
sage: chi.conductor()
pari: znconreyconductor(g,chi)
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Conductor | = | 83 |
sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Order | = | 82 |
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 | = | Odd |
Orbit label | = | 83.d |
Orbit index | = | 4 |
Galois orbit
\(\chi_{83}(2,\cdot)\) \(\chi_{83}(5,\cdot)\) \(\chi_{83}(6,\cdot)\) \(\chi_{83}(8,\cdot)\) \(\chi_{83}(13,\cdot)\) \(\chi_{83}(14,\cdot)\) \(\chi_{83}(15,\cdot)\) \(\chi_{83}(18,\cdot)\) \(\chi_{83}(19,\cdot)\) \(\chi_{83}(20,\cdot)\) \(\chi_{83}(22,\cdot)\) \(\chi_{83}(24,\cdot)\) \(\chi_{83}(32,\cdot)\) \(\chi_{83}(34,\cdot)\) \(\chi_{83}(35,\cdot)\) \(\chi_{83}(39,\cdot)\) \(\chi_{83}(42,\cdot)\) \(\chi_{83}(43,\cdot)\) \(\chi_{83}(45,\cdot)\) \(\chi_{83}(46,\cdot)\) \(\chi_{83}(47,\cdot)\) \(\chi_{83}(50,\cdot)\) \(\chi_{83}(52,\cdot)\) \(\chi_{83}(53,\cdot)\) \(\chi_{83}(54,\cdot)\) \(\chi_{83}(55,\cdot)\) \(\chi_{83}(56,\cdot)\) \(\chi_{83}(57,\cdot)\) \(\chi_{83}(58,\cdot)\) \(\chi_{83}(60,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{19}{82}\right)\)
Values
-1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
\(-1\) | \(1\) | \(e\left(\frac{19}{82}\right)\) | \(e\left(\frac{28}{41}\right)\) | \(e\left(\frac{19}{41}\right)\) | \(e\left(\frac{21}{82}\right)\) | \(e\left(\frac{75}{82}\right)\) | \(e\left(\frac{35}{41}\right)\) | \(e\left(\frac{57}{82}\right)\) | \(e\left(\frac{15}{41}\right)\) | \(e\left(\frac{20}{41}\right)\) | \(e\left(\frac{23}{41}\right)\) |
Related number fields
Field of values | \(\Q(\zeta_{41})\) |