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.ga
\(\chi_{4015}(127,\cdot)\) \(\chi_{4015}(238,\cdot)\) \(\chi_{4015}(327,\cdot)\) \(\chi_{4015}(403,\cdot)\) \(\chi_{4015}(413,\cdot)\) \(\chi_{4015}(492,\cdot)\) \(\chi_{4015}(523,\cdot)\) \(\chi_{4015}(778,\cdot)\) \(\chi_{4015}(888,\cdot)\) \(\chi_{4015}(937,\cdot)\) \(\chi_{4015}(1047,\cdot)\) \(\chi_{4015}(1118,\cdot)\) \(\chi_{4015}(1162,\cdot)\) \(\chi_{4015}(1333,\cdot)\) \(\chi_{4015}(1393,\cdot)\) \(\chi_{4015}(1437,\cdot)\) \(\chi_{4015}(1498,\cdot)\) \(\chi_{4015}(1667,\cdot)\) \(\chi_{4015}(1777,\cdot)\) \(\chi_{4015}(2032,\cdot)\) \(\chi_{4015}(2063,\cdot)\) \(\chi_{4015}(2142,\cdot)\) \(\chi_{4015}(2152,\cdot)\) \(\chi_{4015}(2213,\cdot)\) \(\chi_{4015}(2228,\cdot)\) \(\chi_{4015}(2257,\cdot)\) \(\chi_{4015}(2317,\cdot)\) \(\chi_{4015}(2428,\cdot)\) \(\chi_{4015}(2488,\cdot)\) \(\chi_{4015}(2532,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{180})$ |
| Fixed field: | Number field defined by a degree 180 polynomial (not computed) |
Values on generators
\((1607,2191,881)\) → \((i,e\left(\frac{9}{10}\right),e\left(\frac{13}{36}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(127, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{180}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{7}{90}\right)\) | \(e\left(\frac{7}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{7}{30}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{91}{180}\right)\) |