Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(8015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.fm
\(\chi_{8015}(4,\cdot)\) \(\chi_{8015}(354,\cdot)\) \(\chi_{8015}(634,\cdot)\) \(\chi_{8015}(984,\cdot)\) \(\chi_{8015}(1024,\cdot)\) \(\chi_{8015}(1129,\cdot)\) \(\chi_{8015}(1614,\cdot)\) \(\chi_{8015}(1789,\cdot)\) \(\chi_{8015}(2004,\cdot)\) \(\chi_{8015}(2034,\cdot)\) \(\chi_{8015}(2354,\cdot)\) \(\chi_{8015}(2459,\cdot)\) \(\chi_{8015}(2704,\cdot)\) \(\chi_{8015}(2774,\cdot)\) \(\chi_{8015}(3189,\cdot)\) \(\chi_{8015}(3439,\cdot)\) \(\chi_{8015}(3679,\cdot)\) \(\chi_{8015}(3789,\cdot)\) \(\chi_{8015}(4069,\cdot)\) \(\chi_{8015}(4309,\cdot)\) \(\chi_{8015}(4419,\cdot)\) \(\chi_{8015}(4519,\cdot)\) \(\chi_{8015}(5049,\cdot)\) \(\chi_{8015}(5224,\cdot)\) \(\chi_{8015}(5469,\cdot)\) \(\chi_{8015}(5604,\cdot)\) \(\chi_{8015}(5709,\cdot)\) \(\chi_{8015}(6584,\cdot)\) \(\chi_{8015}(6624,\cdot)\) \(\chi_{8015}(6934,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{7}{38}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{101}{114}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{46}{57}\right)\) |