Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(1603\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(228\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1603}(6,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.gk
\(\chi_{8015}(6,\cdot)\) \(\chi_{8015}(41,\cdot)\) \(\chi_{8015}(321,\cdot)\) \(\chi_{8015}(356,\cdot)\) \(\chi_{8015}(391,\cdot)\) \(\chi_{8015}(496,\cdot)\) \(\chi_{8015}(531,\cdot)\) \(\chi_{8015}(811,\cdot)\) \(\chi_{8015}(881,\cdot)\) \(\chi_{8015}(951,\cdot)\) \(\chi_{8015}(1021,\cdot)\) \(\chi_{8015}(1301,\cdot)\) \(\chi_{8015}(1336,\cdot)\) \(\chi_{8015}(1441,\cdot)\) \(\chi_{8015}(1476,\cdot)\) \(\chi_{8015}(1511,\cdot)\) \(\chi_{8015}(1791,\cdot)\) \(\chi_{8015}(1826,\cdot)\) \(\chi_{8015}(1861,\cdot)\) \(\chi_{8015}(2071,\cdot)\) \(\chi_{8015}(2211,\cdot)\) \(\chi_{8015}(2386,\cdot)\) \(\chi_{8015}(2421,\cdot)\) \(\chi_{8015}(2456,\cdot)\) \(\chi_{8015}(2491,\cdot)\) \(\chi_{8015}(2526,\cdot)\) \(\chi_{8015}(2596,\cdot)\) \(\chi_{8015}(2631,\cdot)\) \(\chi_{8015}(2701,\cdot)\) \(\chi_{8015}(2771,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((1,-1,e\left(\frac{1}{228}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{76}\right)\) | \(e\left(\frac{47}{114}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{115}{228}\right)\) | \(e\left(\frac{21}{76}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{1}{76}\right)\) | \(e\left(\frac{7}{19}\right)\) |