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.gz
\(\chi_{8015}(48,\cdot)\) \(\chi_{8015}(83,\cdot)\) \(\chi_{8015}(132,\cdot)\) \(\chi_{8015}(153,\cdot)\) \(\chi_{8015}(167,\cdot)\) \(\chi_{8015}(412,\cdot)\) \(\chi_{8015}(587,\cdot)\) \(\chi_{8015}(762,\cdot)\) \(\chi_{8015}(867,\cdot)\) \(\chi_{8015}(1007,\cdot)\) \(\chi_{8015}(1042,\cdot)\) \(\chi_{8015}(1112,\cdot)\) \(\chi_{8015}(1133,\cdot)\) \(\chi_{8015}(1182,\cdot)\) \(\chi_{8015}(1518,\cdot)\) \(\chi_{8015}(1532,\cdot)\) \(\chi_{8015}(1567,\cdot)\) \(\chi_{8015}(1623,\cdot)\) \(\chi_{8015}(1658,\cdot)\) \(\chi_{8015}(2232,\cdot)\) \(\chi_{8015}(2372,\cdot)\) \(\chi_{8015}(2463,\cdot)\) \(\chi_{8015}(2533,\cdot)\) \(\chi_{8015}(2743,\cdot)\) \(\chi_{8015}(2757,\cdot)\) \(\chi_{8015}(2897,\cdot)\) \(\chi_{8015}(2932,\cdot)\) \(\chi_{8015}(3002,\cdot)\) \(\chi_{8015}(3058,\cdot)\) \(\chi_{8015}(3107,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-i,-1,e\left(\frac{16}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(48, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{76}\right)\) | \(e\left(\frac{31}{228}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{89}{114}\right)\) | \(e\left(\frac{71}{76}\right)\) | \(e\left(\frac{31}{114}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{97}{228}\right)\) | \(e\left(\frac{45}{76}\right)\) | \(e\left(\frac{11}{19}\right)\) |