Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(1603\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(114\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1603}(767,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.fe
\(\chi_{8015}(226,\cdot)\) \(\chi_{8015}(291,\cdot)\) \(\chi_{8015}(891,\cdot)\) \(\chi_{8015}(921,\cdot)\) \(\chi_{8015}(961,\cdot)\) \(\chi_{8015}(1131,\cdot)\) \(\chi_{8015}(1201,\cdot)\) \(\chi_{8015}(1661,\cdot)\) \(\chi_{8015}(2006,\cdot)\) \(\chi_{8015}(2041,\cdot)\) \(\chi_{8015}(2146,\cdot)\) \(\chi_{8015}(2711,\cdot)\) \(\chi_{8015}(2781,\cdot)\) \(\chi_{8015}(2851,\cdot)\) \(\chi_{8015}(3026,\cdot)\) \(\chi_{8015}(3306,\cdot)\) \(\chi_{8015}(3481,\cdot)\) \(\chi_{8015}(3511,\cdot)\) \(\chi_{8015}(3761,\cdot)\) \(\chi_{8015}(3971,\cdot)\) \(\chi_{8015}(4041,\cdot)\) \(\chi_{8015}(4561,\cdot)\) \(\chi_{8015}(5156,\cdot)\) \(\chi_{8015}(5366,\cdot)\) \(\chi_{8015}(5576,\cdot)\) \(\chi_{8015}(5716,\cdot)\) \(\chi_{8015}(5966,\cdot)\) \(\chi_{8015}(6101,\cdot)\) \(\chi_{8015}(6906,\cdot)\) \(\chi_{8015}(6941,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{57})$ |
| Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((1,e\left(\frac{2}{3}\right),e\left(\frac{91}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(5576, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{114}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{91}{114}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{22}{57}\right)\) |