Basic properties
| Modulus: | \(4015\) | |
| Conductor: | \(365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{365}(78,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4015.ev
\(\chi_{4015}(78,\cdot)\) \(\chi_{4015}(177,\cdot)\) \(\chi_{4015}(232,\cdot)\) \(\chi_{4015}(672,\cdot)\) \(\chi_{4015}(848,\cdot)\) \(\chi_{4015}(1123,\cdot)\) \(\chi_{4015}(1893,\cdot)\) \(\chi_{4015}(2058,\cdot)\) \(\chi_{4015}(2102,\cdot)\) \(\chi_{4015}(2223,\cdot)\) \(\chi_{4015}(2443,\cdot)\) \(\chi_{4015}(2542,\cdot)\) \(\chi_{4015}(2597,\cdot)\) \(\chi_{4015}(2608,\cdot)\) \(\chi_{4015}(2982,\cdot)\) \(\chi_{4015}(3037,\cdot)\) \(\chi_{4015}(3092,\cdot)\) \(\chi_{4015}(3378,\cdot)\) \(\chi_{4015}(3543,\cdot)\) \(\chi_{4015}(3697,\cdot)\) \(\chi_{4015}(3752,\cdot)\) \(\chi_{4015}(3763,\cdot)\) \(\chi_{4015}(3807,\cdot)\) \(\chi_{4015}(3928,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((1607,2191,881)\) → \((-i,1,e\left(\frac{1}{72}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(78, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{5}{72}\right)\) | \(e\left(\frac{5}{72}\right)\) |