Basic properties
| Modulus: | \(4015\) | |
| Conductor: | \(803\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{803}(181,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4015.ft
\(\chi_{4015}(181,\cdot)\) \(\chi_{4015}(196,\cdot)\) \(\chi_{4015}(311,\cdot)\) \(\chi_{4015}(346,\cdot)\) \(\chi_{4015}(476,\cdot)\) \(\chi_{4015}(676,\cdot)\) \(\chi_{4015}(841,\cdot)\) \(\chi_{4015}(851,\cdot)\) \(\chi_{4015}(911,\cdot)\) \(\chi_{4015}(961,\cdot)\) \(\chi_{4015}(1016,\cdot)\) \(\chi_{4015}(1076,\cdot)\) \(\chi_{4015}(1191,\cdot)\) \(\chi_{4015}(1291,\cdot)\) \(\chi_{4015}(1406,\cdot)\) \(\chi_{4015}(1466,\cdot)\) \(\chi_{4015}(1521,\cdot)\) \(\chi_{4015}(1556,\cdot)\) \(\chi_{4015}(1571,\cdot)\) \(\chi_{4015}(1631,\cdot)\) \(\chi_{4015}(1831,\cdot)\) \(\chi_{4015}(1886,\cdot)\) \(\chi_{4015}(1996,\cdot)\) \(\chi_{4015}(2006,\cdot)\) \(\chi_{4015}(2171,\cdot)\) \(\chi_{4015}(2286,\cdot)\) \(\chi_{4015}(2501,\cdot)\) \(\chi_{4015}(2561,\cdot)\) \(\chi_{4015}(2616,\cdot)\) \(\chi_{4015}(2666,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((1,e\left(\frac{2}{5}\right),e\left(\frac{17}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(181, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{16}{45}\right)\) | \(e\left(\frac{19}{90}\right)\) | \(e\left(\frac{23}{60}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{7}{18}\right)\) | \(e\left(\frac{47}{180}\right)\) | \(e\left(\frac{101}{180}\right)\) |