Basic properties
| Modulus: | \(4067\) | |
| Conductor: | \(581\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(246\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{581}(31,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4067.x
\(\chi_{4067}(31,\cdot)\) \(\chi_{4067}(68,\cdot)\) \(\chi_{4067}(178,\cdot)\) \(\chi_{4067}(215,\cdot)\) \(\chi_{4067}(227,\cdot)\) \(\chi_{4067}(276,\cdot)\) \(\chi_{4067}(313,\cdot)\) \(\chi_{4067}(362,\cdot)\) \(\chi_{4067}(509,\cdot)\) \(\chi_{4067}(521,\cdot)\) \(\chi_{4067}(607,\cdot)\) \(\chi_{4067}(619,\cdot)\) \(\chi_{4067}(656,\cdot)\) \(\chi_{4067}(668,\cdot)\) \(\chi_{4067}(705,\cdot)\) \(\chi_{4067}(754,\cdot)\) \(\chi_{4067}(815,\cdot)\) \(\chi_{4067}(950,\cdot)\) \(\chi_{4067}(962,\cdot)\) \(\chi_{4067}(999,\cdot)\) \(\chi_{4067}(1060,\cdot)\) \(\chi_{4067}(1109,\cdot)\) \(\chi_{4067}(1195,\cdot)\) \(\chi_{4067}(1256,\cdot)\) \(\chi_{4067}(1293,\cdot)\) \(\chi_{4067}(1354,\cdot)\) \(\chi_{4067}(1391,\cdot)\) \(\chi_{4067}(1403,\cdot)\) \(\chi_{4067}(1440,\cdot)\) \(\chi_{4067}(1452,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{123})$ |
| Fixed field: | Number field defined by a degree 246 polynomial (not computed) |
Values on generators
\((2159,2990)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{19}{41}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 4067 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{98}{123}\right)\) | \(e\left(\frac{131}{246}\right)\) | \(e\left(\frac{73}{123}\right)\) | \(e\left(\frac{85}{246}\right)\) | \(e\left(\frac{27}{82}\right)\) | \(e\left(\frac{16}{41}\right)\) | \(e\left(\frac{8}{123}\right)\) | \(e\left(\frac{35}{246}\right)\) | \(e\left(\frac{97}{123}\right)\) | \(e\left(\frac{31}{246}\right)\) |