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 | = | 124 |
| Real | = | no |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | yes |
| Minimal | = | yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
| Parity | = | odd |
| Orbit label | = | 373.j |
| Orbit index | = | 10 |
Galois orbit
\(\chi_{373}(8,\cdot)\) \(\chi_{373}(18,\cdot)\) \(\chi_{373}(19,\cdot)\) \(\chi_{373}(20,\cdot)\) \(\chi_{373}(23,\cdot)\) \(\chi_{373}(33,\cdot)\) \(\chi_{373}(45,\cdot)\) \(\chi_{373}(50,\cdot)\) \(\chi_{373}(56,\cdot)\) \(\chi_{373}(58,\cdot)\) \(\chi_{373}(67,\cdot)\) \(\chi_{373}(74,\cdot)\) \(\chi_{373}(96,\cdot)\) \(\chi_{373}(97,\cdot)\) \(\chi_{373}(113,\cdot)\) \(\chi_{373}(125,\cdot)\) \(\chi_{373}(126,\cdot)\) \(\chi_{373}(129,\cdot)\) \(\chi_{373}(133,\cdot)\) \(\chi_{373}(136,\cdot)\) \(\chi_{373}(139,\cdot)\) \(\chi_{373}(140,\cdot)\) \(\chi_{373}(142,\cdot)\) \(\chi_{373}(145,\cdot)\) \(\chi_{373}(146,\cdot)\) \(\chi_{373}(157,\cdot)\) \(\chi_{373}(161,\cdot)\) \(\chi_{373}(167,\cdot)\) \(\chi_{373}(176,\cdot)\) \(\chi_{373}(185,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{57}{124}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(-1\) | \(1\) | \(e\left(\frac{57}{124}\right)\) | \(e\left(\frac{25}{62}\right)\) | \(e\left(\frac{57}{62}\right)\) | \(e\left(\frac{85}{124}\right)\) | \(e\left(\frac{107}{124}\right)\) | \(e\left(\frac{1}{62}\right)\) | \(e\left(\frac{47}{124}\right)\) | \(e\left(\frac{25}{31}\right)\) | \(e\left(\frac{9}{62}\right)\) | \(e\left(\frac{77}{124}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{124})\) |