Basic properties
| Modulus: | \(5269\) | |
| Conductor: | \(479\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(478\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{479}(34,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5269.j
\(\chi_{5269}(34,\cdot)\) \(\chi_{5269}(67,\cdot)\) \(\chi_{5269}(78,\cdot)\) \(\chi_{5269}(111,\cdot)\) \(\chi_{5269}(133,\cdot)\) \(\chi_{5269}(155,\cdot)\) \(\chi_{5269}(166,\cdot)\) \(\chi_{5269}(177,\cdot)\) \(\chi_{5269}(188,\cdot)\) \(\chi_{5269}(199,\cdot)\) \(\chi_{5269}(232,\cdot)\) \(\chi_{5269}(254,\cdot)\) \(\chi_{5269}(265,\cdot)\) \(\chi_{5269}(287,\cdot)\) \(\chi_{5269}(298,\cdot)\) \(\chi_{5269}(342,\cdot)\) \(\chi_{5269}(353,\cdot)\) \(\chi_{5269}(364,\cdot)\) \(\chi_{5269}(408,\cdot)\) \(\chi_{5269}(419,\cdot)\) \(\chi_{5269}(430,\cdot)\) \(\chi_{5269}(452,\cdot)\) \(\chi_{5269}(463,\cdot)\) \(\chi_{5269}(474,\cdot)\) \(\chi_{5269}(496,\cdot)\) \(\chi_{5269}(518,\cdot)\) \(\chi_{5269}(562,\cdot)\) \(\chi_{5269}(573,\cdot)\) \(\chi_{5269}(595,\cdot)\) \(\chi_{5269}(606,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{239})$ |
| Fixed field: | Number field defined by a degree 478 polynomial (not computed) |
Values on generators
\((959,4324)\) → \((1,e\left(\frac{121}{478}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 5269 }(34, a) \) | \(-1\) | \(1\) | \(e\left(\frac{152}{239}\right)\) | \(e\left(\frac{215}{239}\right)\) | \(e\left(\frac{65}{239}\right)\) | \(e\left(\frac{220}{239}\right)\) | \(e\left(\frac{128}{239}\right)\) | \(e\left(\frac{32}{239}\right)\) | \(e\left(\frac{217}{239}\right)\) | \(e\left(\frac{191}{239}\right)\) | \(e\left(\frac{133}{239}\right)\) | \(e\left(\frac{41}{239}\right)\) |