Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
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| Conductor | = | 6027 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 420 |
| 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 | = | 6027.er |
| Orbit index | = | 122 |
Galois orbit
\(\chi_{6027}(5,\cdot)\) \(\chi_{6027}(131,\cdot)\) \(\chi_{6027}(143,\cdot)\) \(\chi_{6027}(185,\cdot)\) \(\chi_{6027}(248,\cdot)\) \(\chi_{6027}(320,\cdot)\) \(\chi_{6027}(446,\cdot)\) \(\chi_{6027}(500,\cdot)\) \(\chi_{6027}(572,\cdot)\) \(\chi_{6027}(635,\cdot)\) \(\chi_{6027}(677,\cdot)\) \(\chi_{6027}(689,\cdot)\) \(\chi_{6027}(740,\cdot)\) \(\chi_{6027}(866,\cdot)\) \(\chi_{6027}(941,\cdot)\) \(\chi_{6027}(992,\cdot)\) \(\chi_{6027}(1004,\cdot)\) \(\chi_{6027}(1046,\cdot)\) \(\chi_{6027}(1181,\cdot)\) \(\chi_{6027}(1235,\cdot)\) \(\chi_{6027}(1307,\cdot)\) \(\chi_{6027}(1361,\cdot)\) \(\chi_{6027}(1433,\cdot)\) \(\chi_{6027}(1496,\cdot)\) \(\chi_{6027}(1601,\cdot)\) \(\chi_{6027}(1676,\cdot)\) \(\chi_{6027}(1727,\cdot)\) \(\chi_{6027}(1802,\cdot)\) \(\chi_{6027}(1853,\cdot)\) \(\chi_{6027}(1865,\cdot)\) ...
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{29}{42}\right),e\left(\frac{11}{20}\right))\)
Values
| -1 | 1 | 2 | 4 | 5 | 8 | 10 | 11 | 13 | 16 | 17 | 19 |
| \(1\) | \(1\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{131}{210}\right)\) | \(e\left(\frac{9}{35}\right)\) | \(e\left(\frac{79}{210}\right)\) | \(e\left(\frac{323}{420}\right)\) | \(e\left(\frac{117}{140}\right)\) | \(e\left(\frac{1}{105}\right)\) | \(e\left(\frac{383}{420}\right)\) | \(e\left(\frac{7}{60}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{420})\) |