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 | = | 372 |
| Real | = | no |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
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| Primitive | = | yes |
| Minimal | = | yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
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| Parity | = | odd |
| Orbit label | = | 373.l |
| Orbit index | = | 12 |
Galois orbit
\(\chi_{373}(2,\cdot)\) \(\chi_{373}(5,\cdot)\) \(\chi_{373}(6,\cdot)\) \(\chi_{373}(11,\cdot)\) \(\chi_{373}(14,\cdot)\) \(\chi_{373}(15,\cdot)\) \(\chi_{373}(24,\cdot)\) \(\chi_{373}(26,\cdot)\) \(\chi_{373}(32,\cdot)\) \(\chi_{373}(34,\cdot)\) \(\chi_{373}(35,\cdot)\) \(\chi_{373}(42,\cdot)\) \(\chi_{373}(43,\cdot)\) \(\chi_{373}(44,\cdot)\) \(\chi_{373}(47,\cdot)\) \(\chi_{373}(53,\cdot)\) \(\chi_{373}(54,\cdot)\) \(\chi_{373}(57,\cdot)\) \(\chi_{373}(60,\cdot)\) \(\chi_{373}(61,\cdot)\) \(\chi_{373}(62,\cdot)\) \(\chi_{373}(65,\cdot)\) \(\chi_{373}(72,\cdot)\) \(\chi_{373}(76,\cdot)\) \(\chi_{373}(77,\cdot)\) \(\chi_{373}(78,\cdot)\) \(\chi_{373}(79,\cdot)\) \(\chi_{373}(80,\cdot)\) \(\chi_{373}(82,\cdot)\) \(\chi_{373}(85,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{35}{372}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(-1\) | \(1\) | \(e\left(\frac{35}{372}\right)\) | \(e\left(\frac{73}{186}\right)\) | \(e\left(\frac{35}{186}\right)\) | \(e\left(\frac{335}{372}\right)\) | \(e\left(\frac{181}{372}\right)\) | \(e\left(\frac{39}{62}\right)\) | \(e\left(\frac{35}{124}\right)\) | \(e\left(\frac{73}{93}\right)\) | \(e\left(\frac{185}{186}\right)\) | \(e\left(\frac{19}{372}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{372})\) |