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.hm
\(\chi_{8015}(23,\cdot)\) \(\chi_{8015}(163,\cdot)\) \(\chi_{8015}(268,\cdot)\) \(\chi_{8015}(298,\cdot)\) \(\chi_{8015}(303,\cdot)\) \(\chi_{8015}(697,\cdot)\) \(\chi_{8015}(718,\cdot)\) \(\chi_{8015}(842,\cdot)\) \(\chi_{8015}(877,\cdot)\) \(\chi_{8015}(982,\cdot)\) \(\chi_{8015}(1033,\cdot)\) \(\chi_{8015}(1117,\cdot)\) \(\chi_{8015}(1122,\cdot)\) \(\chi_{8015}(1138,\cdot)\) \(\chi_{8015}(1152,\cdot)\) \(\chi_{8015}(1173,\cdot)\) \(\chi_{8015}(1257,\cdot)\) \(\chi_{8015}(1437,\cdot)\) \(\chi_{8015}(1472,\cdot)\) \(\chi_{8015}(1507,\cdot)\) \(\chi_{8015}(1572,\cdot)\) \(\chi_{8015}(1593,\cdot)\) \(\chi_{8015}(1808,\cdot)\) \(\chi_{8015}(1992,\cdot)\) \(\chi_{8015}(2032,\cdot)\) \(\chi_{8015}(2328,\cdot)\) \(\chi_{8015}(2382,\cdot)\) \(\chi_{8015}(2403,\cdot)\) \(\chi_{8015}(2417,\cdot)\) \(\chi_{8015}(2853,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-i,e\left(\frac{1}{3}\right),e\left(\frac{109}{228}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{5}{228}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{109}{228}\right)\) | \(e\left(\frac{7}{19}\right)\) | \(e\left(\frac{5}{114}\right)\) | \(e\left(\frac{89}{114}\right)\) | \(e\left(\frac{71}{76}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{47}{57}\right)\) |