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.fi
\(\chi_{8015}(9,\cdot)\) \(\chi_{8015}(149,\cdot)\) \(\chi_{8015}(359,\cdot)\) \(\chi_{8015}(569,\cdot)\) \(\chi_{8015}(1164,\cdot)\) \(\chi_{8015}(1684,\cdot)\) \(\chi_{8015}(1754,\cdot)\) \(\chi_{8015}(1964,\cdot)\) \(\chi_{8015}(2214,\cdot)\) \(\chi_{8015}(2244,\cdot)\) \(\chi_{8015}(2419,\cdot)\) \(\chi_{8015}(2699,\cdot)\) \(\chi_{8015}(2874,\cdot)\) \(\chi_{8015}(2944,\cdot)\) \(\chi_{8015}(3014,\cdot)\) \(\chi_{8015}(3579,\cdot)\) \(\chi_{8015}(3684,\cdot)\) \(\chi_{8015}(3719,\cdot)\) \(\chi_{8015}(4064,\cdot)\) \(\chi_{8015}(4524,\cdot)\) \(\chi_{8015}(4594,\cdot)\) \(\chi_{8015}(4764,\cdot)\) \(\chi_{8015}(4804,\cdot)\) \(\chi_{8015}(4834,\cdot)\) \(\chi_{8015}(5434,\cdot)\) \(\chi_{8015}(5499,\cdot)\) \(\chi_{8015}(5884,\cdot)\) \(\chi_{8015}(6029,\cdot)\) \(\chi_{8015}(6234,\cdot)\) \(\chi_{8015}(6274,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{47}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{13}{19}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{35}{114}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{53}{57}\right)\) |