Basic properties
| Modulus: | \(4015\) | |
| Conductor: | \(4015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(360\) | 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 4015.gj
\(\chi_{4015}(29,\cdot)\) \(\chi_{4015}(39,\cdot)\) \(\chi_{4015}(84,\cdot)\) \(\chi_{4015}(204,\cdot)\) \(\chi_{4015}(239,\cdot)\) \(\chi_{4015}(259,\cdot)\) \(\chi_{4015}(354,\cdot)\) \(\chi_{4015}(404,\cdot)\) \(\chi_{4015}(409,\cdot)\) \(\chi_{4015}(424,\cdot)\) \(\chi_{4015}(464,\cdot)\) \(\chi_{4015}(469,\cdot)\) \(\chi_{4015}(524,\cdot)\) \(\chi_{4015}(569,\cdot)\) \(\chi_{4015}(579,\cdot)\) \(\chi_{4015}(589,\cdot)\) \(\chi_{4015}(624,\cdot)\) \(\chi_{4015}(629,\cdot)\) \(\chi_{4015}(644,\cdot)\) \(\chi_{4015}(699,\cdot)\) \(\chi_{4015}(744,\cdot)\) \(\chi_{4015}(789,\cdot)\) \(\chi_{4015}(904,\cdot)\) \(\chi_{4015}(909,\cdot)\) \(\chi_{4015}(954,\cdot)\) \(\chi_{4015}(964,\cdot)\) \(\chi_{4015}(1009,\cdot)\) \(\chi_{4015}(1064,\cdot)\) \(\chi_{4015}(1069,\cdot)\) \(\chi_{4015}(1084,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{360})$ |
| Fixed field: | Number field defined by a degree 360 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((-1,e\left(\frac{7}{10}\right),e\left(\frac{35}{72}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(29, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{45}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{19}{180}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{317}{360}\right)\) | \(e\left(\frac{191}{360}\right)\) |