Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 751 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 125 |
| Real | = | No |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | No |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
| Parity | = | Even |
| Orbit label | = | 6008.bp |
| Orbit index | = | 42 |
Galois orbit
\(\chi_{6008}(49,\cdot)\) \(\chi_{6008}(185,\cdot)\) \(\chi_{6008}(249,\cdot)\) \(\chi_{6008}(305,\cdot)\) \(\chi_{6008}(433,\cdot)\) \(\chi_{6008}(457,\cdot)\) \(\chi_{6008}(545,\cdot)\) \(\chi_{6008}(617,\cdot)\) \(\chi_{6008}(681,\cdot)\) \(\chi_{6008}(729,\cdot)\) \(\chi_{6008}(745,\cdot)\) \(\chi_{6008}(761,\cdot)\) \(\chi_{6008}(777,\cdot)\) \(\chi_{6008}(793,\cdot)\) \(\chi_{6008}(905,\cdot)\) \(\chi_{6008}(1145,\cdot)\) \(\chi_{6008}(1241,\cdot)\) \(\chi_{6008}(1281,\cdot)\) \(\chi_{6008}(1329,\cdot)\) \(\chi_{6008}(1345,\cdot)\) \(\chi_{6008}(1545,\cdot)\) \(\chi_{6008}(1689,\cdot)\) \(\chi_{6008}(1849,\cdot)\) \(\chi_{6008}(1921,\cdot)\) \(\chi_{6008}(1937,\cdot)\) \(\chi_{6008}(2025,\cdot)\) \(\chi_{6008}(2033,\cdot)\) \(\chi_{6008}(2097,\cdot)\) \(\chi_{6008}(2129,\cdot)\) \(\chi_{6008}(2185,\cdot)\) ...
Inducing primitive character
Values on generators
\((1503,3005,1505)\) → \((1,1,e\left(\frac{92}{125}\right))\)
Values
| -1 | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 |
| \(1\) | \(1\) | \(e\left(\frac{92}{125}\right)\) | \(e\left(\frac{87}{125}\right)\) | \(e\left(\frac{17}{125}\right)\) | \(e\left(\frac{59}{125}\right)\) | \(e\left(\frac{6}{25}\right)\) | \(e\left(\frac{111}{125}\right)\) | \(e\left(\frac{54}{125}\right)\) | \(e\left(\frac{18}{125}\right)\) | \(e\left(\frac{31}{125}\right)\) | \(e\left(\frac{109}{125}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{125})\) |