Basic properties
| Modulus: | \(4761\) | |
| Conductor: | \(4761\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(138\) | 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 4761.x
\(\chi_{4761}(22,\cdot)\) \(\chi_{4761}(160,\cdot)\) \(\chi_{4761}(229,\cdot)\) \(\chi_{4761}(367,\cdot)\) \(\chi_{4761}(436,\cdot)\) \(\chi_{4761}(574,\cdot)\) \(\chi_{4761}(643,\cdot)\) \(\chi_{4761}(781,\cdot)\) \(\chi_{4761}(850,\cdot)\) \(\chi_{4761}(988,\cdot)\) \(\chi_{4761}(1195,\cdot)\) \(\chi_{4761}(1264,\cdot)\) \(\chi_{4761}(1402,\cdot)\) \(\chi_{4761}(1471,\cdot)\) \(\chi_{4761}(1609,\cdot)\) \(\chi_{4761}(1678,\cdot)\) \(\chi_{4761}(1816,\cdot)\) \(\chi_{4761}(1885,\cdot)\) \(\chi_{4761}(2023,\cdot)\) \(\chi_{4761}(2092,\cdot)\) \(\chi_{4761}(2230,\cdot)\) \(\chi_{4761}(2299,\cdot)\) \(\chi_{4761}(2437,\cdot)\) \(\chi_{4761}(2506,\cdot)\) \(\chi_{4761}(2713,\cdot)\) \(\chi_{4761}(2851,\cdot)\) \(\chi_{4761}(2920,\cdot)\) \(\chi_{4761}(3058,\cdot)\) \(\chi_{4761}(3127,\cdot)\) \(\chi_{4761}(3265,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{69})$ |
| Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((2117,1063)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{45}{46}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 4761 }(160, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{69}\right)\) | \(e\left(\frac{44}{69}\right)\) | \(e\left(\frac{43}{138}\right)\) | \(e\left(\frac{119}{138}\right)\) | \(e\left(\frac{22}{23}\right)\) | \(e\left(\frac{29}{46}\right)\) | \(e\left(\frac{125}{138}\right)\) | \(e\left(\frac{14}{69}\right)\) | \(e\left(\frac{25}{138}\right)\) | \(e\left(\frac{19}{69}\right)\) |