Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 1007 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 468 |
| 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 | = | 6042.cr |
| Orbit index | = | 70 |
Galois orbit
\(\chi_{6042}(55,\cdot)\) \(\chi_{6042}(61,\cdot)\) \(\chi_{6042}(73,\cdot)\) \(\chi_{6042}(85,\cdot)\) \(\chi_{6042}(139,\cdot)\) \(\chi_{6042}(157,\cdot)\) \(\chi_{6042}(253,\cdot)\) \(\chi_{6042}(283,\cdot)\) \(\chi_{6042}(313,\cdot)\) \(\chi_{6042}(385,\cdot)\) \(\chi_{6042}(397,\cdot)\) \(\chi_{6042}(403,\cdot)\) \(\chi_{6042}(427,\cdot)\) \(\chi_{6042}(499,\cdot)\) \(\chi_{6042}(511,\cdot)\) \(\chi_{6042}(595,\cdot)\) \(\chi_{6042}(631,\cdot)\) \(\chi_{6042}(655,\cdot)\) \(\chi_{6042}(709,\cdot)\) \(\chi_{6042}(739,\cdot)\) \(\chi_{6042}(745,\cdot)\) \(\chi_{6042}(769,\cdot)\) \(\chi_{6042}(853,\cdot)\) \(\chi_{6042}(883,\cdot)\) \(\chi_{6042}(973,\cdot)\) \(\chi_{6042}(985,\cdot)\) \(\chi_{6042}(1081,\cdot)\) \(\chi_{6042}(1087,\cdot)\) \(\chi_{6042}(1099,\cdot)\) \(\chi_{6042}(1111,\cdot)\) ...
Inducing primitive character
Values on generators
\((2015,4771,2281)\) → \((1,e\left(\frac{1}{9}\right),e\left(\frac{3}{52}\right))\)
Values
| -1 | 1 | 5 | 7 | 11 | 13 | 17 | 23 | 25 | 29 | 31 | 35 |
| \(-1\) | \(1\) | \(e\left(\frac{229}{468}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{110}{117}\right)\) | \(e\left(\frac{161}{234}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{229}{234}\right)\) | \(e\left(\frac{127}{234}\right)\) | \(e\left(\frac{89}{156}\right)\) | \(e\left(\frac{451}{468}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{468})\) |