Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(229\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{229}(36,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.fv
\(\chi_{8015}(36,\cdot)\) \(\chi_{8015}(71,\cdot)\) \(\chi_{8015}(421,\cdot)\) \(\chi_{8015}(491,\cdot)\) \(\chi_{8015}(561,\cdot)\) \(\chi_{8015}(596,\cdot)\) \(\chi_{8015}(736,\cdot)\) \(\chi_{8015}(841,\cdot)\) \(\chi_{8015}(1016,\cdot)\) \(\chi_{8015}(1191,\cdot)\) \(\chi_{8015}(1436,\cdot)\) \(\chi_{8015}(1471,\cdot)\) \(\chi_{8015}(1681,\cdot)\) \(\chi_{8015}(1751,\cdot)\) \(\chi_{8015}(2066,\cdot)\) \(\chi_{8015}(2276,\cdot)\) \(\chi_{8015}(2346,\cdot)\) \(\chi_{8015}(3151,\cdot)\) \(\chi_{8015}(3186,\cdot)\) \(\chi_{8015}(3291,\cdot)\) \(\chi_{8015}(3676,\cdot)\) \(\chi_{8015}(4656,\cdot)\) \(\chi_{8015}(4726,\cdot)\) \(\chi_{8015}(4761,\cdot)\) \(\chi_{8015}(5216,\cdot)\) \(\chi_{8015}(5566,\cdot)\) \(\chi_{8015}(5706,\cdot)\) \(\chi_{8015}(5951,\cdot)\) \(\chi_{8015}(6301,\cdot)\) \(\chi_{8015}(6511,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((1,1,e\left(\frac{1}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{1}{114}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{37}{57}\right)\) | \(e\left(\frac{8}{19}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{14}{19}\right)\) |