Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 6008 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 750 |
| Real | = | No |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | Yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
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| Parity | = | Even |
| Orbit label | = | 6008.ch |
| Orbit index | = | 60 |
Galois orbit
\(\chi_{6008}(5,\cdot)\) \(\chi_{6008}(13,\cdot)\) \(\chi_{6008}(21,\cdot)\) \(\chi_{6008}(37,\cdot)\) \(\chi_{6008}(77,\cdot)\) \(\chi_{6008}(109,\cdot)\) \(\chi_{6008}(149,\cdot)\) \(\chi_{6008}(181,\cdot)\) \(\chi_{6008}(245,\cdot)\) \(\chi_{6008}(269,\cdot)\) \(\chi_{6008}(309,\cdot)\) \(\chi_{6008}(333,\cdot)\) \(\chi_{6008}(397,\cdot)\) \(\chi_{6008}(461,\cdot)\) \(\chi_{6008}(469,\cdot)\) \(\chi_{6008}(477,\cdot)\) \(\chi_{6008}(549,\cdot)\) \(\chi_{6008}(581,\cdot)\) \(\chi_{6008}(613,\cdot)\) \(\chi_{6008}(669,\cdot)\) \(\chi_{6008}(853,\cdot)\) \(\chi_{6008}(893,\cdot)\) \(\chi_{6008}(925,\cdot)\) \(\chi_{6008}(965,\cdot)\) \(\chi_{6008}(981,\cdot)\) \(\chi_{6008}(989,\cdot)\) \(\chi_{6008}(1029,\cdot)\) \(\chi_{6008}(1053,\cdot)\) \(\chi_{6008}(1077,\cdot)\) \(\chi_{6008}(1093,\cdot)\) ...
Values on generators
\((1503,3005,1505)\) → \((1,-1,e\left(\frac{368}{375}\right))\)
Values
| -1 | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 |
| \(1\) | \(1\) | \(e\left(\frac{361}{750}\right)\) | \(e\left(\frac{571}{750}\right)\) | \(e\left(\frac{106}{125}\right)\) | \(e\left(\frac{361}{375}\right)\) | \(e\left(\frac{23}{150}\right)\) | \(e\left(\frac{13}{750}\right)\) | \(e\left(\frac{91}{375}\right)\) | \(e\left(\frac{322}{375}\right)\) | \(e\left(\frac{373}{750}\right)\) | \(e\left(\frac{247}{750}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{375})\) |