Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 6027 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 210 |
| 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)
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| Parity | = | even |
| Orbit label | = | 6027.ei |
| Orbit index | = | 113 |
Galois orbit
\(\chi_{6027}(236,\cdot)\) \(\chi_{6027}(269,\cdot)\) \(\chi_{6027}(332,\cdot)\) \(\chi_{6027}(353,\cdot)\) \(\chi_{6027}(605,\cdot)\) \(\chi_{6027}(761,\cdot)\) \(\chi_{6027}(824,\cdot)\) \(\chi_{6027}(845,\cdot)\) \(\chi_{6027}(1130,\cdot)\) \(\chi_{6027}(1193,\cdot)\) \(\chi_{6027}(1214,\cdot)\) \(\chi_{6027}(1466,\cdot)\) \(\chi_{6027}(1622,\cdot)\) \(\chi_{6027}(1706,\cdot)\) \(\chi_{6027}(1958,\cdot)\) \(\chi_{6027}(2054,\cdot)\) \(\chi_{6027}(2075,\cdot)\) \(\chi_{6027}(2327,\cdot)\) \(\chi_{6027}(2483,\cdot)\) \(\chi_{6027}(2546,\cdot)\) \(\chi_{6027}(2819,\cdot)\) \(\chi_{6027}(2852,\cdot)\) \(\chi_{6027}(2915,\cdot)\) \(\chi_{6027}(2936,\cdot)\) \(\chi_{6027}(3188,\cdot)\) \(\chi_{6027}(3344,\cdot)\) \(\chi_{6027}(3407,\cdot)\) \(\chi_{6027}(3428,\cdot)\) \(\chi_{6027}(3680,\cdot)\) \(\chi_{6027}(3713,\cdot)\) ...
Values on generators
\((4019,493,2794)\) → \((-1,e\left(\frac{23}{42}\right),e\left(\frac{7}{10}\right))\)
Values
| -1 | 1 | 2 | 4 | 5 | 8 | 10 | 11 | 13 | 16 | 17 | 19 |
| \(1\) | \(1\) | \(e\left(\frac{197}{210}\right)\) | \(e\left(\frac{92}{105}\right)\) | \(e\left(\frac{82}{105}\right)\) | \(e\left(\frac{57}{70}\right)\) | \(e\left(\frac{151}{210}\right)\) | \(e\left(\frac{53}{105}\right)\) | \(e\left(\frac{27}{35}\right)\) | \(e\left(\frac{79}{105}\right)\) | \(e\left(\frac{61}{210}\right)\) | \(e\left(\frac{7}{15}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{105})\) |