Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 503 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 251 |
| 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 | = | 4024.i |
| Orbit index | = | 9 |
Galois orbit
\(\chi_{4024}(9,\cdot)\) \(\chi_{4024}(25,\cdot)\) \(\chi_{4024}(33,\cdot)\) \(\chi_{4024}(49,\cdot)\) \(\chi_{4024}(73,\cdot)\) \(\chi_{4024}(81,\cdot)\) \(\chi_{4024}(97,\cdot)\) \(\chi_{4024}(113,\cdot)\) \(\chi_{4024}(121,\cdot)\) \(\chi_{4024}(129,\cdot)\) \(\chi_{4024}(145,\cdot)\) \(\chi_{4024}(161,\cdot)\) \(\chi_{4024}(169,\cdot)\) \(\chi_{4024}(177,\cdot)\) \(\chi_{4024}(185,\cdot)\) \(\chi_{4024}(201,\cdot)\) \(\chi_{4024}(225,\cdot)\) \(\chi_{4024}(233,\cdot)\) \(\chi_{4024}(249,\cdot)\) \(\chi_{4024}(257,\cdot)\) \(\chi_{4024}(265,\cdot)\) \(\chi_{4024}(273,\cdot)\) \(\chi_{4024}(281,\cdot)\) \(\chi_{4024}(289,\cdot)\) \(\chi_{4024}(297,\cdot)\) \(\chi_{4024}(329,\cdot)\) \(\chi_{4024}(361,\cdot)\) \(\chi_{4024}(393,\cdot)\) \(\chi_{4024}(401,\cdot)\) \(\chi_{4024}(433,\cdot)\) ...
Inducing primitive character
Values on generators
\((1007,2013,2017)\) → \((1,1,e\left(\frac{156}{251}\right))\)
Values
| -1 | 1 | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 |
| \(1\) | \(1\) | \(e\left(\frac{240}{251}\right)\) | \(e\left(\frac{156}{251}\right)\) | \(e\left(\frac{113}{251}\right)\) | \(e\left(\frac{229}{251}\right)\) | \(e\left(\frac{26}{251}\right)\) | \(e\left(\frac{17}{251}\right)\) | \(e\left(\frac{145}{251}\right)\) | \(e\left(\frac{82}{251}\right)\) | \(e\left(\frac{75}{251}\right)\) | \(e\left(\frac{102}{251}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{251})\) |