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 \(\chi_{365}(133,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4015.fb
\(\chi_{4015}(133,\cdot)\) \(\chi_{4015}(188,\cdot)\) \(\chi_{4015}(287,\cdot)\) \(\chi_{4015}(452,\cdot)\) \(\chi_{4015}(573,\cdot)\) \(\chi_{4015}(617,\cdot)\) \(\chi_{4015}(628,\cdot)\) \(\chi_{4015}(683,\cdot)\) \(\chi_{4015}(837,\cdot)\) \(\chi_{4015}(1002,\cdot)\) \(\chi_{4015}(1288,\cdot)\) \(\chi_{4015}(1343,\cdot)\) \(\chi_{4015}(1398,\cdot)\) \(\chi_{4015}(1772,\cdot)\) \(\chi_{4015}(1783,\cdot)\) \(\chi_{4015}(1838,\cdot)\) \(\chi_{4015}(1937,\cdot)\) \(\chi_{4015}(2157,\cdot)\) \(\chi_{4015}(2278,\cdot)\) \(\chi_{4015}(2322,\cdot)\) \(\chi_{4015}(2487,\cdot)\) \(\chi_{4015}(3257,\cdot)\) \(\chi_{4015}(3532,\cdot)\) \(\chi_{4015}(3708,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((1607,2191,881)\) → \((-i,1,e\left(\frac{23}{72}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(133, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{7}{72}\right)\) | \(e\left(\frac{43}{72}\right)\) |