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.hb
\(\chi_{8015}(62,\cdot)\) \(\chi_{8015}(97,\cdot)\) \(\chi_{8015}(118,\cdot)\) \(\chi_{8015}(307,\cdot)\) \(\chi_{8015}(328,\cdot)\) \(\chi_{8015}(377,\cdot)\) \(\chi_{8015}(433,\cdot)\) \(\chi_{8015}(503,\cdot)\) \(\chi_{8015}(538,\cdot)\) \(\chi_{8015}(678,\cdot)\) \(\chi_{8015}(692,\cdot)\) \(\chi_{8015}(902,\cdot)\) \(\chi_{8015}(972,\cdot)\) \(\chi_{8015}(1063,\cdot)\) \(\chi_{8015}(1203,\cdot)\) \(\chi_{8015}(1777,\cdot)\) \(\chi_{8015}(1812,\cdot)\) \(\chi_{8015}(1868,\cdot)\) \(\chi_{8015}(1903,\cdot)\) \(\chi_{8015}(1917,\cdot)\) \(\chi_{8015}(2253,\cdot)\) \(\chi_{8015}(2302,\cdot)\) \(\chi_{8015}(2323,\cdot)\) \(\chi_{8015}(2393,\cdot)\) \(\chi_{8015}(2428,\cdot)\) \(\chi_{8015}(2568,\cdot)\) \(\chi_{8015}(2673,\cdot)\) \(\chi_{8015}(2848,\cdot)\) \(\chi_{8015}(3023,\cdot)\) \(\chi_{8015}(3268,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((i,-1,e\left(\frac{25}{114}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(62, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{76}\right)\) | \(e\left(\frac{197}{228}\right)\) | \(e\left(\frac{27}{38}\right)\) | \(e\left(\frac{41}{57}\right)\) | \(e\left(\frac{43}{76}\right)\) | \(e\left(\frac{83}{114}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{131}{228}\right)\) | \(e\left(\frac{69}{76}\right)\) | \(e\left(\frac{8}{19}\right)\) |