Basic properties
| Modulus: | \(5077\) | |
| Conductor: | \(5077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(282\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5077.q
\(\chi_{5077}(22,\cdot)\) \(\chi_{5077}(27,\cdot)\) \(\chi_{5077}(109,\cdot)\) \(\chi_{5077}(120,\cdot)\) \(\chi_{5077}(133,\cdot)\) \(\chi_{5077}(184,\cdot)\) \(\chi_{5077}(195,\cdot)\) \(\chi_{5077}(202,\cdot)\) \(\chi_{5077}(222,\cdot)\) \(\chi_{5077}(299,\cdot)\) \(\chi_{5077}(477,\cdot)\) \(\chi_{5077}(490,\cdot)\) \(\chi_{5077}(526,\cdot)\) \(\chi_{5077}(576,\cdot)\) \(\chi_{5077}(723,\cdot)\) \(\chi_{5077}(745,\cdot)\) \(\chi_{5077}(807,\cdot)\) \(\chi_{5077}(831,\cdot)\) \(\chi_{5077}(849,\cdot)\) \(\chi_{5077}(913,\cdot)\) \(\chi_{5077}(936,\cdot)\) \(\chi_{5077}(1145,\cdot)\) \(\chi_{5077}(1226,\cdot)\) \(\chi_{5077}(1305,\cdot)\) \(\chi_{5077}(1486,\cdot)\) \(\chi_{5077}(1521,\cdot)\) \(\chi_{5077}(1636,\cdot)\) \(\chi_{5077}(1644,\cdot)\) \(\chi_{5077}(1671,\cdot)\) \(\chi_{5077}(1683,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{141})$ |
| Fixed field: | Number field defined by a degree 282 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{163}{282}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 5077 }(27, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{282}\right)\) | \(e\left(\frac{14}{47}\right)\) | \(e\left(\frac{22}{141}\right)\) | \(e\left(\frac{63}{94}\right)\) | \(e\left(\frac{247}{282}\right)\) | \(e\left(\frac{5}{141}\right)\) | \(e\left(\frac{69}{94}\right)\) | \(e\left(\frac{28}{47}\right)\) | \(e\left(\frac{35}{141}\right)\) | \(e\left(\frac{107}{282}\right)\) |