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.fz
\(\chi_{4015}(2,\cdot)\) \(\chi_{4015}(128,\cdot)\) \(\chi_{4015}(162,\cdot)\) \(\chi_{4015}(178,\cdot)\) \(\chi_{4015}(183,\cdot)\) \(\chi_{4015}(347,\cdot)\) \(\chi_{4015}(402,\cdot)\) \(\chi_{4015}(442,\cdot)\) \(\chi_{4015}(513,\cdot)\) \(\chi_{4015}(673,\cdot)\) \(\chi_{4015}(712,\cdot)\) \(\chi_{4015}(732,\cdot)\) \(\chi_{4015}(767,\cdot)\) \(\chi_{4015}(908,\cdot)\) \(\chi_{4015}(953,\cdot)\) \(\chi_{4015}(1097,\cdot)\) \(\chi_{4015}(1172,\cdot)\) \(\chi_{4015}(1223,\cdot)\) \(\chi_{4015}(1273,\cdot)\) \(\chi_{4015}(1278,\cdot)\) \(\chi_{4015}(1403,\cdot)\) \(\chi_{4015}(1492,\cdot)\) \(\chi_{4015}(1537,\cdot)\) \(\chi_{4015}(1608,\cdot)\) \(\chi_{4015}(1768,\cdot)\) \(\chi_{4015}(1953,\cdot)\) \(\chi_{4015}(1987,\cdot)\) \(\chi_{4015}(2008,\cdot)\) \(\chi_{4015}(2048,\cdot)\) \(\chi_{4015}(2318,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((i,e\left(\frac{1}{10}\right),e\left(\frac{1}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{180}\right)\) | \(e\left(\frac{13}{60}\right)\) | \(e\left(\frac{43}{90}\right)\) | \(e\left(\frac{41}{90}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{73}{180}\right)\) | \(e\left(\frac{77}{90}\right)\) |