Basic properties
| Modulus: | \(4015\) | |
| Conductor: | \(803\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{803}(116,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4015.fl
\(\chi_{4015}(116,\cdot)\) \(\chi_{4015}(226,\cdot)\) \(\chi_{4015}(271,\cdot)\) \(\chi_{4015}(431,\cdot)\) \(\chi_{4015}(481,\cdot)\) \(\chi_{4015}(541,\cdot)\) \(\chi_{4015}(591,\cdot)\) \(\chi_{4015}(601,\cdot)\) \(\chi_{4015}(1151,\cdot)\) \(\chi_{4015}(1161,\cdot)\) \(\chi_{4015}(1271,\cdot)\) \(\chi_{4015}(1366,\cdot)\) \(\chi_{4015}(1481,\cdot)\) \(\chi_{4015}(1526,\cdot)\) \(\chi_{4015}(1636,\cdot)\) \(\chi_{4015}(1696,\cdot)\) \(\chi_{4015}(2096,\cdot)\) \(\chi_{4015}(2246,\cdot)\) \(\chi_{4015}(2306,\cdot)\) \(\chi_{4015}(2416,\cdot)\) \(\chi_{4015}(2426,\cdot)\) \(\chi_{4015}(2461,\cdot)\) \(\chi_{4015}(2576,\cdot)\) \(\chi_{4015}(2791,\cdot)\) \(\chi_{4015}(2976,\cdot)\) \(\chi_{4015}(3306,\cdot)\) \(\chi_{4015}(3341,\cdot)\) \(\chi_{4015}(3351,\cdot)\) \(\chi_{4015}(3401,\cdot)\) \(\chi_{4015}(3461,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((1,e\left(\frac{9}{10}\right),e\left(\frac{17}{24}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(116, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{29}{120}\right)\) |