Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(1145\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(228\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1145}(162,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.hq
\(\chi_{8015}(162,\cdot)\) \(\chi_{8015}(253,\cdot)\) \(\chi_{8015}(267,\cdot)\) \(\chi_{8015}(302,\cdot)\) \(\chi_{8015}(722,\cdot)\) \(\chi_{8015}(792,\cdot)\) \(\chi_{8015}(988,\cdot)\) \(\chi_{8015}(1058,\cdot)\) \(\chi_{8015}(1247,\cdot)\) \(\chi_{8015}(1282,\cdot)\) \(\chi_{8015}(1562,\cdot)\) \(\chi_{8015}(1632,\cdot)\) \(\chi_{8015}(1758,\cdot)\) \(\chi_{8015}(1793,\cdot)\) \(\chi_{8015}(1898,\cdot)\) \(\chi_{8015}(1982,\cdot)\) \(\chi_{8015}(2038,\cdot)\) \(\chi_{8015}(2108,\cdot)\) \(\chi_{8015}(2157,\cdot)\) \(\chi_{8015}(2192,\cdot)\) \(\chi_{8015}(2213,\cdot)\) \(\chi_{8015}(2227,\cdot)\) \(\chi_{8015}(2353,\cdot)\) \(\chi_{8015}(2367,\cdot)\) \(\chi_{8015}(2388,\cdot)\) \(\chi_{8015}(2423,\cdot)\) \(\chi_{8015}(2472,\cdot)\) \(\chi_{8015}(2542,\cdot)\) \(\chi_{8015}(2598,\cdot)\) \(\chi_{8015}(2682,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((i,1,e\left(\frac{169}{228}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(162, a) \) | \(1\) | \(1\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{211}{228}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{169}{228}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{97}{114}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{127}{228}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{5}{19}\right)\) |