Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 805 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| 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)
| ||
| Parity | = | Odd |
| Orbit label | = | 4025.cz |
| Orbit index | = | 78 |
Galois orbit
\(\chi_{4025}(18,\cdot)\) \(\chi_{4025}(32,\cdot)\) \(\chi_{4025}(193,\cdot)\) \(\chi_{4025}(282,\cdot)\) \(\chi_{4025}(443,\cdot)\) \(\chi_{4025}(807,\cdot)\) \(\chi_{4025}(968,\cdot)\) \(\chi_{4025}(982,\cdot)\) \(\chi_{4025}(1143,\cdot)\) \(\chi_{4025}(1432,\cdot)\) \(\chi_{4025}(1507,\cdot)\) \(\chi_{4025}(1593,\cdot)\) \(\chi_{4025}(1668,\cdot)\) \(\chi_{4025}(1682,\cdot)\) \(\chi_{4025}(1843,\cdot)\) \(\chi_{4025}(1957,\cdot)\) \(\chi_{4025}(2032,\cdot)\) \(\chi_{4025}(2118,\cdot)\) \(\chi_{4025}(2132,\cdot)\) \(\chi_{4025}(2193,\cdot)\) \(\chi_{4025}(2293,\cdot)\) \(\chi_{4025}(2382,\cdot)\) \(\chi_{4025}(2543,\cdot)\) \(\chi_{4025}(2557,\cdot)\) \(\chi_{4025}(2657,\cdot)\) \(\chi_{4025}(2718,\cdot)\) \(\chi_{4025}(2732,\cdot)\) \(\chi_{4025}(2818,\cdot)\) \(\chi_{4025}(2832,\cdot)\) \(\chi_{4025}(2893,\cdot)\) ...
Inducing primitive character
Values on generators
\((2577,1151,3501)\) → \((i,e\left(\frac{2}{3}\right),e\left(\frac{5}{11}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 6 | 8 | 9 | 11 | 12 | 13 | 16 |
| \(-1\) | \(1\) | \(e\left(\frac{65}{132}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{65}{66}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{21}{44}\right)\) | \(e\left(\frac{25}{66}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{89}{132}\right)\) | \(e\left(\frac{5}{44}\right)\) | \(e\left(\frac{32}{33}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{132})\) |