Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 1340 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
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| Order | = | 132 |
| 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)
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| Parity | = | Odd |
| Orbit label | = | 4020.dr |
| Orbit index | = | 96 |
Galois orbit
\(\chi_{4020}(7,\cdot)\) \(\chi_{4020}(247,\cdot)\) \(\chi_{4020}(367,\cdot)\) \(\chi_{4020}(463,\cdot)\) \(\chi_{4020}(487,\cdot)\) \(\chi_{4020}(547,\cdot)\) \(\chi_{4020}(727,\cdot)\) \(\chi_{4020}(787,\cdot)\) \(\chi_{4020}(883,\cdot)\) \(\chi_{4020}(1123,\cdot)\) \(\chi_{4020}(1183,\cdot)\) \(\chi_{4020}(1267,\cdot)\) \(\chi_{4020}(1543,\cdot)\) \(\chi_{4020}(1687,\cdot)\) \(\chi_{4020}(1723,\cdot)\) \(\chi_{4020}(1783,\cdot)\) \(\chi_{4020}(1843,\cdot)\) \(\chi_{4020}(1927,\cdot)\) \(\chi_{4020}(1963,\cdot)\) \(\chi_{4020}(1987,\cdot)\) \(\chi_{4020}(2023,\cdot)\) \(\chi_{4020}(2347,\cdot)\) \(\chi_{4020}(2443,\cdot)\) \(\chi_{4020}(2527,\cdot)\) \(\chi_{4020}(2587,\cdot)\) \(\chi_{4020}(2647,\cdot)\) \(\chi_{4020}(2743,\cdot)\) \(\chi_{4020}(2767,\cdot)\) \(\chi_{4020}(2827,\cdot)\) \(\chi_{4020}(3043,\cdot)\) ...
Inducing primitive character
Values on generators
\((2011,2681,3217,1141)\) → \((-1,1,i,e\left(\frac{23}{66}\right))\)
Values
| -1 | 1 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 |
| \(-1\) | \(1\) | \(e\left(\frac{101}{132}\right)\) | \(e\left(\frac{2}{33}\right)\) | \(e\left(\frac{49}{132}\right)\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{16}{33}\right)\) | \(e\left(\frac{1}{132}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{31}{66}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{132})\) |