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.he
\(\chi_{8015}(59,\cdot)\) \(\chi_{8015}(164,\cdot)\) \(\chi_{8015}(194,\cdot)\) \(\chi_{8015}(264,\cdot)\) \(\chi_{8015}(269,\cdot)\) \(\chi_{8015}(339,\cdot)\) \(\chi_{8015}(614,\cdot)\) \(\chi_{8015}(754,\cdot)\) \(\chi_{8015}(759,\cdot)\) \(\chi_{8015}(789,\cdot)\) \(\chi_{8015}(824,\cdot)\) \(\chi_{8015}(829,\cdot)\) \(\chi_{8015}(1139,\cdot)\) \(\chi_{8015}(1174,\cdot)\) \(\chi_{8015}(1214,\cdot)\) \(\chi_{8015}(1634,\cdot)\) \(\chi_{8015}(1699,\cdot)\) \(\chi_{8015}(1734,\cdot)\) \(\chi_{8015}(1769,\cdot)\) \(\chi_{8015}(1879,\cdot)\) \(\chi_{8015}(1949,\cdot)\) \(\chi_{8015}(1984,\cdot)\) \(\chi_{8015}(2054,\cdot)\) \(\chi_{8015}(2084,\cdot)\) \(\chi_{8015}(2089,\cdot)\) \(\chi_{8015}(2224,\cdot)\) \(\chi_{8015}(2329,\cdot)\) \(\chi_{8015}(2364,\cdot)\) \(\chi_{8015}(2369,\cdot)\) \(\chi_{8015}(2469,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\((3207,4581,4586)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{53}{228}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(339, a) \) | \(1\) | \(1\) | \(e\left(\frac{163}{228}\right)\) | \(e\left(\frac{1}{57}\right)\) | \(e\left(\frac{49}{114}\right)\) | \(e\left(\frac{167}{228}\right)\) | \(e\left(\frac{11}{76}\right)\) | \(e\left(\frac{2}{57}\right)\) | \(e\left(\frac{37}{114}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{15}{76}\right)\) | \(e\left(\frac{49}{57}\right)\) |