Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(1145\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1145}(904,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.ft
\(\chi_{8015}(904,\cdot)\) \(\chi_{8015}(1289,\cdot)\) \(\chi_{8015}(1394,\cdot)\) \(\chi_{8015}(1429,\cdot)\) \(\chi_{8015}(2234,\cdot)\) \(\chi_{8015}(2304,\cdot)\) \(\chi_{8015}(2514,\cdot)\) \(\chi_{8015}(2829,\cdot)\) \(\chi_{8015}(2899,\cdot)\) \(\chi_{8015}(3109,\cdot)\) \(\chi_{8015}(3144,\cdot)\) \(\chi_{8015}(3389,\cdot)\) \(\chi_{8015}(3564,\cdot)\) \(\chi_{8015}(3739,\cdot)\) \(\chi_{8015}(3844,\cdot)\) \(\chi_{8015}(3984,\cdot)\) \(\chi_{8015}(4019,\cdot)\) \(\chi_{8015}(4089,\cdot)\) \(\chi_{8015}(4159,\cdot)\) \(\chi_{8015}(4509,\cdot)\) \(\chi_{8015}(4544,\cdot)\) \(\chi_{8015}(5209,\cdot)\) \(\chi_{8015}(5349,\cdot)\) \(\chi_{8015}(5734,\cdot)\) \(\chi_{8015}(5874,\cdot)\) \(\chi_{8015}(5909,\cdot)\) \(\chi_{8015}(5979,\cdot)\) \(\chi_{8015}(6084,\cdot)\) \(\chi_{8015}(6294,\cdot)\) \(\chi_{8015}(6644,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-1,1,e\left(\frac{34}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(904, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{65}{114}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{3}{38}\right)\) | \(e\left(\frac{8}{57}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{71}{114}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{2}{19}\right)\) |