Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 1007 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 156 |
| 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 | = | 6042.ch |
| Orbit index | = | 60 |
Galois orbit
\(\chi_{6042}(31,\cdot)\) \(\chi_{6042}(103,\cdot)\) \(\chi_{6042}(145,\cdot)\) \(\chi_{6042}(217,\cdot)\) \(\chi_{6042}(373,\cdot)\) \(\chi_{6042}(445,\cdot)\) \(\chi_{6042}(601,\cdot)\) \(\chi_{6042}(715,\cdot)\) \(\chi_{6042}(787,\cdot)\) \(\chi_{6042}(829,\cdot)\) \(\chi_{6042}(1015,\cdot)\) \(\chi_{6042}(1057,\cdot)\) \(\chi_{6042}(1171,\cdot)\) \(\chi_{6042}(1357,\cdot)\) \(\chi_{6042}(1399,\cdot)\) \(\chi_{6042}(1585,\cdot)\) \(\chi_{6042}(1699,\cdot)\) \(\chi_{6042}(1741,\cdot)\) \(\chi_{6042}(1927,\cdot)\) \(\chi_{6042}(1969,\cdot)\) \(\chi_{6042}(2041,\cdot)\) \(\chi_{6042}(2155,\cdot)\) \(\chi_{6042}(2311,\cdot)\) \(\chi_{6042}(2383,\cdot)\) \(\chi_{6042}(2539,\cdot)\) \(\chi_{6042}(2611,\cdot)\) \(\chi_{6042}(2653,\cdot)\) \(\chi_{6042}(2725,\cdot)\) \(\chi_{6042}(2881,\cdot)\) \(\chi_{6042}(2995,\cdot)\) ...
Inducing primitive character
Values on generators
\((2015,4771,2281)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{43}{52}\right))\)
Values
| -1 | 1 | 5 | 7 | 11 | 13 | 17 | 23 | 25 | 29 | 31 | 35 |
| \(1\) | \(1\) | \(e\left(\frac{83}{156}\right)\) | \(e\left(\frac{15}{26}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{34}{39}\right)\) | \(e\left(\frac{41}{52}\right)\) | \(e\left(\frac{17}{156}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{156})\) |