Basic properties
| Modulus: | \(4015\) | |
| Conductor: | \(4015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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.fm
\(\chi_{4015}(163,\cdot)\) \(\chi_{4015}(262,\cdot)\) \(\chi_{4015}(322,\cdot)\) \(\chi_{4015}(532,\cdot)\) \(\chi_{4015}(687,\cdot)\) \(\chi_{4015}(713,\cdot)\) \(\chi_{4015}(883,\cdot)\) \(\chi_{4015}(1147,\cdot)\) \(\chi_{4015}(1248,\cdot)\) \(\chi_{4015}(1258,\cdot)\) \(\chi_{4015}(1357,\cdot)\) \(\chi_{4015}(1417,\cdot)\) \(\chi_{4015}(1512,\cdot)\) \(\chi_{4015}(1808,\cdot)\) \(\chi_{4015}(1818,\cdot)\) \(\chi_{4015}(1978,\cdot)\) \(\chi_{4015}(2183,\cdot)\) \(\chi_{4015}(2242,\cdot)\) \(\chi_{4015}(2357,\cdot)\) \(\chi_{4015}(2512,\cdot)\) \(\chi_{4015}(2722,\cdot)\) \(\chi_{4015}(2913,\cdot)\) \(\chi_{4015}(3073,\cdot)\) \(\chi_{4015}(3083,\cdot)\) \(\chi_{4015}(3182,\cdot)\) \(\chi_{4015}(3337,\cdot)\) \(\chi_{4015}(3448,\cdot)\) \(\chi_{4015}(3452,\cdot)\) \(\chi_{4015}(3547,\cdot)\) \(\chi_{4015}(3633,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((-i,e\left(\frac{3}{5}\right),e\left(\frac{7}{24}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(163, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{31}{120}\right)\) |