Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(8015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(228\) | 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.gf
\(\chi_{8015}(24,\cdot)\) \(\chi_{8015}(124,\cdot)\) \(\chi_{8015}(334,\cdot)\) \(\chi_{8015}(649,\cdot)\) \(\chi_{8015}(1104,\cdot)\) \(\chi_{8015}(1284,\cdot)\) \(\chi_{8015}(1384,\cdot)\) \(\chi_{8015}(1424,\cdot)\) \(\chi_{8015}(1524,\cdot)\) \(\chi_{8015}(1529,\cdot)\) \(\chi_{8015}(1564,\cdot)\) \(\chi_{8015}(1669,\cdot)\) \(\chi_{8015}(1804,\cdot)\) \(\chi_{8015}(1809,\cdot)\) \(\chi_{8015}(1839,\cdot)\) \(\chi_{8015}(1909,\cdot)\) \(\chi_{8015}(1944,\cdot)\) \(\chi_{8015}(2014,\cdot)\) \(\chi_{8015}(2124,\cdot)\) \(\chi_{8015}(2159,\cdot)\) \(\chi_{8015}(2194,\cdot)\) \(\chi_{8015}(2259,\cdot)\) \(\chi_{8015}(2679,\cdot)\) \(\chi_{8015}(2719,\cdot)\) \(\chi_{8015}(2754,\cdot)\) \(\chi_{8015}(3064,\cdot)\) \(\chi_{8015}(3069,\cdot)\) \(\chi_{8015}(3104,\cdot)\) \(\chi_{8015}(3134,\cdot)\) \(\chi_{8015}(3139,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{43}{228}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(24, a) \) | \(1\) | \(1\) | \(e\left(\frac{181}{228}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{67}{114}\right)\) | \(e\left(\frac{157}{228}\right)\) | \(e\left(\frac{29}{76}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{25}{114}\right)\) | \(e\left(\frac{55}{114}\right)\) | \(e\left(\frac{5}{76}\right)\) | \(e\left(\frac{10}{57}\right)\) |