Basic properties
| Modulus: | \(5077\) | |
| Conductor: | \(5077\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(188\) | 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 5077.p
\(\chi_{5077}(5,\cdot)\) \(\chi_{5077}(68,\cdot)\) \(\chi_{5077}(73,\cdot)\) \(\chi_{5077}(125,\cdot)\) \(\chi_{5077}(206,\cdot)\) \(\chi_{5077}(224,\cdot)\) \(\chi_{5077}(342,\cdot)\) \(\chi_{5077}(364,\cdot)\) \(\chi_{5077}(491,\cdot)\) \(\chi_{5077}(516,\cdot)\) \(\chi_{5077}(523,\cdot)\) \(\chi_{5077}(528,\cdot)\) \(\chi_{5077}(565,\cdot)\) \(\chi_{5077}(601,\cdot)\) \(\chi_{5077}(778,\cdot)\) \(\chi_{5077}(826,\cdot)\) \(\chi_{5077}(965,\cdot)\) \(\chi_{5077}(1038,\cdot)\) \(\chi_{5077}(1054,\cdot)\) \(\chi_{5077}(1106,\cdot)\) \(\chi_{5077}(1142,\cdot)\) \(\chi_{5077}(1260,\cdot)\) \(\chi_{5077}(1407,\cdot)\) \(\chi_{5077}(1520,\cdot)\) \(\chi_{5077}(1604,\cdot)\) \(\chi_{5077}(1605,\cdot)\) \(\chi_{5077}(1700,\cdot)\) \(\chi_{5077}(1825,\cdot)\) \(\chi_{5077}(1884,\cdot)\) \(\chi_{5077}(1905,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{188})$ |
| Fixed field: | Number field defined by a degree 188 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{11}{188}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 5077 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{188}\right)\) | \(e\left(\frac{21}{94}\right)\) | \(e\left(\frac{11}{94}\right)\) | \(e\left(\frac{71}{188}\right)\) | \(e\left(\frac{53}{188}\right)\) | \(e\left(\frac{13}{47}\right)\) | \(e\left(\frac{33}{188}\right)\) | \(e\left(\frac{21}{47}\right)\) | \(e\left(\frac{41}{94}\right)\) | \(e\left(\frac{171}{188}\right)\) |