Basic properties
| Modulus: | \(4015\) | |
| Conductor: | \(803\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(72\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{803}(351,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4015.ez
\(\chi_{4015}(131,\cdot)\) \(\chi_{4015}(186,\cdot)\) \(\chi_{4015}(351,\cdot)\) \(\chi_{4015}(516,\cdot)\) \(\chi_{4015}(571,\cdot)\) \(\chi_{4015}(626,\cdot)\) \(\chi_{4015}(1011,\cdot)\) \(\chi_{4015}(1066,\cdot)\) \(\chi_{4015}(1121,\cdot)\) \(\chi_{4015}(1286,\cdot)\) \(\chi_{4015}(1561,\cdot)\) \(\chi_{4015}(1726,\cdot)\) \(\chi_{4015}(1781,\cdot)\) \(\chi_{4015}(1836,\cdot)\) \(\chi_{4015}(2221,\cdot)\) \(\chi_{4015}(2276,\cdot)\) \(\chi_{4015}(2331,\cdot)\) \(\chi_{4015}(2496,\cdot)\) \(\chi_{4015}(2661,\cdot)\) \(\chi_{4015}(2716,\cdot)\) \(\chi_{4015}(2881,\cdot)\) \(\chi_{4015}(3046,\cdot)\) \(\chi_{4015}(3816,\cdot)\) \(\chi_{4015}(3981,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{72})$ |
| Fixed field: | Number field defined by a degree 72 polynomial |
Values on generators
\((1607,2191,881)\) → \((1,-1,e\left(\frac{5}{72}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 4015 }(351, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{19}{24}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{43}{72}\right)\) | \(e\left(\frac{61}{72}\right)\) |