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 | = | 41 |
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 | = | 83.c |
Orbit index | = | 3 |
Galois orbit
\(\chi_{83}(3,\cdot)\) \(\chi_{83}(4,\cdot)\) \(\chi_{83}(7,\cdot)\) \(\chi_{83}(9,\cdot)\) \(\chi_{83}(10,\cdot)\) \(\chi_{83}(11,\cdot)\) \(\chi_{83}(12,\cdot)\) \(\chi_{83}(16,\cdot)\) \(\chi_{83}(17,\cdot)\) \(\chi_{83}(21,\cdot)\) \(\chi_{83}(23,\cdot)\) \(\chi_{83}(25,\cdot)\) \(\chi_{83}(26,\cdot)\) \(\chi_{83}(27,\cdot)\) \(\chi_{83}(28,\cdot)\) \(\chi_{83}(29,\cdot)\) \(\chi_{83}(30,\cdot)\) \(\chi_{83}(31,\cdot)\) \(\chi_{83}(33,\cdot)\) \(\chi_{83}(36,\cdot)\) \(\chi_{83}(37,\cdot)\) \(\chi_{83}(38,\cdot)\) \(\chi_{83}(40,\cdot)\) \(\chi_{83}(41,\cdot)\) \(\chi_{83}(44,\cdot)\) \(\chi_{83}(48,\cdot)\) \(\chi_{83}(49,\cdot)\) \(\chi_{83}(51,\cdot)\) \(\chi_{83}(59,\cdot)\) \(\chi_{83}(61,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{13}{41}\right)\)
Values
-1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
\(1\) | \(1\) | \(e\left(\frac{13}{41}\right)\) | \(e\left(\frac{34}{41}\right)\) | \(e\left(\frac{26}{41}\right)\) | \(e\left(\frac{23}{41}\right)\) | \(e\left(\frac{6}{41}\right)\) | \(e\left(\frac{22}{41}\right)\) | \(e\left(\frac{39}{41}\right)\) | \(e\left(\frac{27}{41}\right)\) | \(e\left(\frac{36}{41}\right)\) | \(e\left(\frac{25}{41}\right)\) |
Related number fields
Field of values | \(\Q(\zeta_{41})\) |