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.fx
\(\chi_{4015}(18,\cdot)\) \(\chi_{4015}(57,\cdot)\) \(\chi_{4015}(182,\cdot)\) \(\chi_{4015}(217,\cdot)\) \(\chi_{4015}(237,\cdot)\) \(\chi_{4015}(288,\cdot)\) \(\chi_{4015}(547,\cdot)\) \(\chi_{4015}(552,\cdot)\) \(\chi_{4015}(568,\cdot)\) \(\chi_{4015}(602,\cdot)\) \(\chi_{4015}(728,\cdot)\) \(\chi_{4015}(787,\cdot)\) \(\chi_{4015}(1018,\cdot)\) \(\chi_{4015}(1058,\cdot)\) \(\chi_{4015}(1063,\cdot)\) \(\chi_{4015}(1113,\cdot)\) \(\chi_{4015}(1152,\cdot)\) \(\chi_{4015}(1282,\cdot)\) \(\chi_{4015}(1383,\cdot)\) \(\chi_{4015}(1458,\cdot)\) \(\chi_{4015}(1602,\cdot)\) \(\chi_{4015}(1647,\cdot)\) \(\chi_{4015}(1663,\cdot)\) \(\chi_{4015}(1788,\cdot)\) \(\chi_{4015}(1823,\cdot)\) \(\chi_{4015}(1843,\cdot)\) \(\chi_{4015}(2042,\cdot)\) \(\chi_{4015}(2153,\cdot)\) \(\chi_{4015}(2158,\cdot)\) \(\chi_{4015}(2208,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((-i,e\left(\frac{7}{10}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{121}{180}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{31}{90}\right)\) | \(e\left(\frac{17}{90}\right)\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{1}{30}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{61}{180}\right)\) | \(e\left(\frac{22}{45}\right)\) |