Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 373 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 186 |
| 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 | = | 373.k |
| Orbit index | = | 11 |
Galois orbit
\(\chi_{373}(3,\cdot)\) \(\chi_{373}(4,\cdot)\) \(\chi_{373}(10,\cdot)\) \(\chi_{373}(25,\cdot)\) \(\chi_{373}(36,\cdot)\) \(\chi_{373}(37,\cdot)\) \(\chi_{373}(48,\cdot)\) \(\chi_{373}(59,\cdot)\) \(\chi_{373}(63,\cdot)\) \(\chi_{373}(71,\cdot)\) \(\chi_{373}(90,\cdot)\) \(\chi_{373}(103,\cdot)\) \(\chi_{373}(106,\cdot)\) \(\chi_{373}(112,\cdot)\) \(\chi_{373}(114,\cdot)\) \(\chi_{373}(116,\cdot)\) \(\chi_{373}(117,\cdot)\) \(\chi_{373}(120,\cdot)\) \(\chi_{373}(121,\cdot)\) \(\chi_{373}(122,\cdot)\) \(\chi_{373}(123,\cdot)\) \(\chi_{373}(134,\cdot)\) \(\chi_{373}(138,\cdot)\) \(\chi_{373}(147,\cdot)\) \(\chi_{373}(153,\cdot)\) \(\chi_{373}(164,\cdot)\) \(\chi_{373}(181,\cdot)\) \(\chi_{373}(194,\cdot)\) \(\chi_{373}(196,\cdot)\) \(\chi_{373}(198,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{119}{186}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{119}{186}\right)\) | \(e\left(\frac{25}{93}\right)\) | \(e\left(\frac{26}{93}\right)\) | \(e\left(\frac{23}{186}\right)\) | \(e\left(\frac{169}{186}\right)\) | \(e\left(\frac{21}{31}\right)\) | \(e\left(\frac{57}{62}\right)\) | \(e\left(\frac{50}{93}\right)\) | \(e\left(\frac{71}{93}\right)\) | \(e\left(\frac{139}{186}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{93})\) |