Basic properties
| Modulus: | \(5269\) | |
| Conductor: | \(5269\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(478\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5269.l
\(\chi_{5269}(10,\cdot)\) \(\chi_{5269}(21,\cdot)\) \(\chi_{5269}(32,\cdot)\) \(\chi_{5269}(54,\cdot)\) \(\chi_{5269}(98,\cdot)\) \(\chi_{5269}(109,\cdot)\) \(\chi_{5269}(120,\cdot)\) \(\chi_{5269}(131,\cdot)\) \(\chi_{5269}(142,\cdot)\) \(\chi_{5269}(175,\cdot)\) \(\chi_{5269}(197,\cdot)\) \(\chi_{5269}(219,\cdot)\) \(\chi_{5269}(230,\cdot)\) \(\chi_{5269}(241,\cdot)\) \(\chi_{5269}(252,\cdot)\) \(\chi_{5269}(274,\cdot)\) \(\chi_{5269}(307,\cdot)\) \(\chi_{5269}(362,\cdot)\) \(\chi_{5269}(373,\cdot)\) \(\chi_{5269}(384,\cdot)\) \(\chi_{5269}(417,\cdot)\) \(\chi_{5269}(428,\cdot)\) \(\chi_{5269}(450,\cdot)\) \(\chi_{5269}(483,\cdot)\) \(\chi_{5269}(494,\cdot)\) \(\chi_{5269}(527,\cdot)\) \(\chi_{5269}(549,\cdot)\) \(\chi_{5269}(560,\cdot)\) \(\chi_{5269}(571,\cdot)\) \(\chi_{5269}(582,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{239})$ |
| Fixed field: | Number field defined by a degree 478 polynomial (not computed) |
Values on generators
\((959,4324)\) → \((-1,e\left(\frac{9}{239}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 5269 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{63}{478}\right)\) | \(e\left(\frac{190}{239}\right)\) | \(e\left(\frac{63}{239}\right)\) | \(e\left(\frac{11}{239}\right)\) | \(e\left(\frac{443}{478}\right)\) | \(e\left(\frac{51}{478}\right)\) | \(e\left(\frac{189}{478}\right)\) | \(e\left(\frac{141}{239}\right)\) | \(e\left(\frac{85}{478}\right)\) | \(e\left(\frac{14}{239}\right)\) |