Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 367 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 61 |
| 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 | = | 367.e |
| Orbit index | = | 5 |
Galois orbit
\(\chi_{367}(7,\cdot)\) \(\chi_{367}(8,\cdot)\) \(\chi_{367}(9,\cdot)\) \(\chi_{367}(15,\cdot)\) \(\chi_{367}(25,\cdot)\) \(\chi_{367}(46,\cdot)\) \(\chi_{367}(47,\cdot)\) \(\chi_{367}(49,\cdot)\) \(\chi_{367}(52,\cdot)\) \(\chi_{367}(56,\cdot)\) \(\chi_{367}(59,\cdot)\) \(\chi_{367}(63,\cdot)\) \(\chi_{367}(64,\cdot)\) \(\chi_{367}(72,\cdot)\) \(\chi_{367}(74,\cdot)\) \(\chi_{367}(81,\cdot)\) \(\chi_{367}(87,\cdot)\) \(\chi_{367}(101,\cdot)\) \(\chi_{367}(105,\cdot)\) \(\chi_{367}(106,\cdot)\) \(\chi_{367}(107,\cdot)\) \(\chi_{367}(114,\cdot)\) \(\chi_{367}(120,\cdot)\) \(\chi_{367}(122,\cdot)\) \(\chi_{367}(124,\cdot)\) \(\chi_{367}(132,\cdot)\) \(\chi_{367}(134,\cdot)\) \(\chi_{367}(135,\cdot)\) \(\chi_{367}(137,\cdot)\) \(\chi_{367}(145,\cdot)\) ...
Values on generators
\(6\) → \(e\left(\frac{40}{61}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{29}{61}\right)\) | \(e\left(\frac{11}{61}\right)\) | \(e\left(\frac{58}{61}\right)\) | \(e\left(\frac{5}{61}\right)\) | \(e\left(\frac{40}{61}\right)\) | \(e\left(\frac{53}{61}\right)\) | \(e\left(\frac{26}{61}\right)\) | \(e\left(\frac{22}{61}\right)\) | \(e\left(\frac{34}{61}\right)\) | \(e\left(\frac{54}{61}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{61})\) |