Basic properties
| Modulus: | \(4015\) | |
| Conductor: | \(803\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(45\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{803}(16,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4015.ei
\(\chi_{4015}(16,\cdot)\) \(\chi_{4015}(201,\cdot)\) \(\chi_{4015}(251,\cdot)\) \(\chi_{4015}(256,\cdot)\) \(\chi_{4015}(566,\cdot)\) \(\chi_{4015}(586,\cdot)\) \(\chi_{4015}(621,\cdot)\) \(\chi_{4015}(746,\cdot)\) \(\chi_{4015}(951,\cdot)\) \(\chi_{4015}(1026,\cdot)\) \(\chi_{4015}(1296,\cdot)\) \(\chi_{4015}(1346,\cdot)\) \(\chi_{4015}(1351,\cdot)\) \(\chi_{4015}(1391,\cdot)\) \(\chi_{4015}(1681,\cdot)\) \(\chi_{4015}(1841,\cdot)\) \(\chi_{4015}(2121,\cdot)\) \(\chi_{4015}(2391,\cdot)\) \(\chi_{4015}(2446,\cdot)\) \(\chi_{4015}(2776,\cdot)\) \(\chi_{4015}(3171,\cdot)\) \(\chi_{4015}(3216,\cdot)\) \(\chi_{4015}(3536,\cdot)\) \(\chi_{4015}(3666,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{45})$ |
| Fixed field: | Number field defined by a degree 45 polynomial |
Values on generators
\((1607,2191,881)\) → \((1,e\left(\frac{2}{5}\right),e\left(\frac{4}{9}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{45}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{41}{45}\right)\) | \(e\left(\frac{37}{45}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{28}{45}\right)\) | \(e\left(\frac{19}{45}\right)\) |