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.gc
\(\chi_{4015}(169,\cdot)\) \(\chi_{4015}(269,\cdot)\) \(\chi_{4015}(444,\cdot)\) \(\chi_{4015}(499,\cdot)\) \(\chi_{4015}(559,\cdot)\) \(\chi_{4015}(609,\cdot)\) \(\chi_{4015}(619,\cdot)\) \(\chi_{4015}(669,\cdot)\) \(\chi_{4015}(724,\cdot)\) \(\chi_{4015}(784,\cdot)\) \(\chi_{4015}(984,\cdot)\) \(\chi_{4015}(999,\cdot)\) \(\chi_{4015}(1114,\cdot)\) \(\chi_{4015}(1149,\cdot)\) \(\chi_{4015}(1279,\cdot)\) \(\chi_{4015}(1479,\cdot)\) \(\chi_{4015}(1644,\cdot)\) \(\chi_{4015}(1654,\cdot)\) \(\chi_{4015}(1714,\cdot)\) \(\chi_{4015}(1764,\cdot)\) \(\chi_{4015}(1819,\cdot)\) \(\chi_{4015}(1879,\cdot)\) \(\chi_{4015}(1994,\cdot)\) \(\chi_{4015}(2094,\cdot)\) \(\chi_{4015}(2209,\cdot)\) \(\chi_{4015}(2269,\cdot)\) \(\chi_{4015}(2324,\cdot)\) \(\chi_{4015}(2359,\cdot)\) \(\chi_{4015}(2374,\cdot)\) \(\chi_{4015}(2434,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{23}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{90}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{67}{90}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{5}{9}\right)\) | \(e\left(\frac{71}{180}\right)\) | \(e\left(\frac{143}{180}\right)\) |