Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(1603\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(76\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1603}(216,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.er
\(\chi_{8015}(216,\cdot)\) \(\chi_{8015}(251,\cdot)\) \(\chi_{8015}(426,\cdot)\) \(\chi_{8015}(601,\cdot)\) \(\chi_{8015}(741,\cdot)\) \(\chi_{8015}(1091,\cdot)\) \(\chi_{8015}(1231,\cdot)\) \(\chi_{8015}(1406,\cdot)\) \(\chi_{8015}(1581,\cdot)\) \(\chi_{8015}(1616,\cdot)\) \(\chi_{8015}(2176,\cdot)\) \(\chi_{8015}(2841,\cdot)\) \(\chi_{8015}(2876,\cdot)\) \(\chi_{8015}(3086,\cdot)\) \(\chi_{8015}(3401,\cdot)\) \(\chi_{8015}(3541,\cdot)\) \(\chi_{8015}(3576,\cdot)\) \(\chi_{8015}(3716,\cdot)\) \(\chi_{8015}(3891,\cdot)\) \(\chi_{8015}(4101,\cdot)\) \(\chi_{8015}(4206,\cdot)\) \(\chi_{8015}(4381,\cdot)\) \(\chi_{8015}(4801,\cdot)\) \(\chi_{8015}(5046,\cdot)\) \(\chi_{8015}(5466,\cdot)\) \(\chi_{8015}(5641,\cdot)\) \(\chi_{8015}(5746,\cdot)\) \(\chi_{8015}(5956,\cdot)\) \(\chi_{8015}(6131,\cdot)\) \(\chi_{8015}(6271,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{76})$ |
| Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((3207,4581,4586)\) → \((1,-1,e\left(\frac{1}{76}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(216, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{76}\right)\) | \(e\left(\frac{9}{38}\right)\) | \(e\left(\frac{21}{38}\right)\) | \(e\left(\frac{39}{76}\right)\) | \(e\left(\frac{63}{76}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{5}{38}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{3}{76}\right)\) | \(e\left(\frac{2}{19}\right)\) |