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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.ei
\(\chi_{8015}(13,\cdot)\) \(\chi_{8015}(237,\cdot)\) \(\chi_{8015}(832,\cdot)\) \(\chi_{8015}(937,\cdot)\) \(\chi_{8015}(1238,\cdot)\) \(\chi_{8015}(1497,\cdot)\) \(\chi_{8015}(1938,\cdot)\) \(\chi_{8015}(2197,\cdot)\) \(\chi_{8015}(2498,\cdot)\) \(\chi_{8015}(2603,\cdot)\) \(\chi_{8015}(3198,\cdot)\) \(\chi_{8015}(3422,\cdot)\) \(\chi_{8015}(3457,\cdot)\) \(\chi_{8015}(3632,\cdot)\) \(\chi_{8015}(3807,\cdot)\) \(\chi_{8015}(3863,\cdot)\) \(\chi_{8015}(4297,\cdot)\) \(\chi_{8015}(4353,\cdot)\) \(\chi_{8015}(4528,\cdot)\) \(\chi_{8015}(4668,\cdot)\) \(\chi_{8015}(4843,\cdot)\) \(\chi_{8015}(5158,\cdot)\) \(\chi_{8015}(5368,\cdot)\) \(\chi_{8015}(5382,\cdot)\) \(\chi_{8015}(6068,\cdot)\) \(\chi_{8015}(6082,\cdot)\) \(\chi_{8015}(6292,\cdot)\) \(\chi_{8015}(6607,\cdot)\) \(\chi_{8015}(6782,\cdot)\) \(\chi_{8015}(6922,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{76})$ |
| Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((3207,4581,4586)\) → \((-i,-1,e\left(\frac{39}{76}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{37}{76}\right)\) | \(e\left(\frac{1}{19}\right)\) | \(e\left(\frac{1}{76}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{37}{38}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{41}{76}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{2}{19}\right)\) |