Basic properties
| Modulus: | \(4015\) | |
| Conductor: | \(4015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(180\) | 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.fu
\(\chi_{4015}(123,\cdot)\) \(\chi_{4015}(457,\cdot)\) \(\chi_{4015}(578,\cdot)\) \(\chi_{4015}(607,\cdot)\) \(\chi_{4015}(622,\cdot)\) \(\chi_{4015}(822,\cdot)\) \(\chi_{4015}(838,\cdot)\) \(\chi_{4015}(853,\cdot)\) \(\chi_{4015}(882,\cdot)\) \(\chi_{4015}(943,\cdot)\) \(\chi_{4015}(987,\cdot)\) \(\chi_{4015}(997,\cdot)\) \(\chi_{4015}(1003,\cdot)\) \(\chi_{4015}(1107,\cdot)\) \(\chi_{4015}(1218,\cdot)\) \(\chi_{4015}(1337,\cdot)\) \(\chi_{4015}(1448,\cdot)\) \(\chi_{4015}(1558,\cdot)\) \(\chi_{4015}(1568,\cdot)\) \(\chi_{4015}(1612,\cdot)\) \(\chi_{4015}(1702,\cdot)\) \(\chi_{4015}(1733,\cdot)\) \(\chi_{4015}(1933,\cdot)\) \(\chi_{4015}(1977,\cdot)\) \(\chi_{4015}(2092,\cdot)\) \(\chi_{4015}(2098,\cdot)\) \(\chi_{4015}(2202,\cdot)\) \(\chi_{4015}(2543,\cdot)\) \(\chi_{4015}(2647,\cdot)\) \(\chi_{4015}(2653,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((-i,e\left(\frac{1}{10}\right),e\left(\frac{5}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(123, a) \) | \(1\) | \(1\) | \(e\left(\frac{173}{180}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{83}{90}\right)\) | \(e\left(\frac{38}{45}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{49}{90}\right)\) | \(e\left(\frac{179}{180}\right)\) |