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.hg
\(\chi_{8015}(69,\cdot)\) \(\chi_{8015}(139,\cdot)\) \(\chi_{8015}(279,\cdot)\) \(\chi_{8015}(384,\cdot)\) \(\chi_{8015}(419,\cdot)\) \(\chi_{8015}(489,\cdot)\) \(\chi_{8015}(524,\cdot)\) \(\chi_{8015}(664,\cdot)\) \(\chi_{8015}(734,\cdot)\) \(\chi_{8015}(804,\cdot)\) \(\chi_{8015}(839,\cdot)\) \(\chi_{8015}(909,\cdot)\) \(\chi_{8015}(944,\cdot)\) \(\chi_{8015}(979,\cdot)\) \(\chi_{8015}(1014,\cdot)\) \(\chi_{8015}(1049,\cdot)\) \(\chi_{8015}(1224,\cdot)\) \(\chi_{8015}(1364,\cdot)\) \(\chi_{8015}(1574,\cdot)\) \(\chi_{8015}(1609,\cdot)\) \(\chi_{8015}(1644,\cdot)\) \(\chi_{8015}(1924,\cdot)\) \(\chi_{8015}(1959,\cdot)\) \(\chi_{8015}(1994,\cdot)\) \(\chi_{8015}(2099,\cdot)\) \(\chi_{8015}(2134,\cdot)\) \(\chi_{8015}(2414,\cdot)\) \(\chi_{8015}(2484,\cdot)\) \(\chi_{8015}(2554,\cdot)\) \(\chi_{8015}(2624,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-1,-1,e\left(\frac{89}{228}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(69, a) \) | \(1\) | \(1\) | \(e\left(\frac{53}{76}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{203}{228}\right)\) | \(e\left(\frac{7}{76}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{67}{114}\right)\) | \(e\left(\frac{51}{76}\right)\) | \(e\left(\frac{15}{19}\right)\) |