Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(8015\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(76\) | 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.el
\(\chi_{8015}(34,\cdot)\) \(\chi_{8015}(349,\cdot)\) \(\chi_{8015}(559,\cdot)\) \(\chi_{8015}(594,\cdot)\) \(\chi_{8015}(1259,\cdot)\) \(\chi_{8015}(1819,\cdot)\) \(\chi_{8015}(1854,\cdot)\) \(\chi_{8015}(2029,\cdot)\) \(\chi_{8015}(2204,\cdot)\) \(\chi_{8015}(2344,\cdot)\) \(\chi_{8015}(2694,\cdot)\) \(\chi_{8015}(2834,\cdot)\) \(\chi_{8015}(3009,\cdot)\) \(\chi_{8015}(3184,\cdot)\) \(\chi_{8015}(3219,\cdot)\) \(\chi_{8015}(3779,\cdot)\) \(\chi_{8015}(4444,\cdot)\) \(\chi_{8015}(4479,\cdot)\) \(\chi_{8015}(4689,\cdot)\) \(\chi_{8015}(5004,\cdot)\) \(\chi_{8015}(5144,\cdot)\) \(\chi_{8015}(5179,\cdot)\) \(\chi_{8015}(5319,\cdot)\) \(\chi_{8015}(5494,\cdot)\) \(\chi_{8015}(5704,\cdot)\) \(\chi_{8015}(5809,\cdot)\) \(\chi_{8015}(5984,\cdot)\) \(\chi_{8015}(6404,\cdot)\) \(\chi_{8015}(6649,\cdot)\) \(\chi_{8015}(7069,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{76})$ |
| Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((3207,4581,4586)\) → \((-1,-1,e\left(\frac{27}{76}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(34, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{76}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{65}{76}\right)\) | \(e\left(\frac{67}{76}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{43}{76}\right)\) | \(e\left(\frac{16}{19}\right)\) |