Basic properties
| Modulus: | \(8015\) | |
| Conductor: | \(1145\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(76\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1145}(22,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8015.ej
\(\chi_{8015}(22,\cdot)\) \(\chi_{8015}(197,\cdot)\) \(\chi_{8015}(372,\cdot)\) \(\chi_{8015}(428,\cdot)\) \(\chi_{8015}(862,\cdot)\) \(\chi_{8015}(918,\cdot)\) \(\chi_{8015}(1093,\cdot)\) \(\chi_{8015}(1233,\cdot)\) \(\chi_{8015}(1408,\cdot)\) \(\chi_{8015}(1723,\cdot)\) \(\chi_{8015}(1933,\cdot)\) \(\chi_{8015}(1947,\cdot)\) \(\chi_{8015}(2633,\cdot)\) \(\chi_{8015}(2647,\cdot)\) \(\chi_{8015}(2857,\cdot)\) \(\chi_{8015}(3172,\cdot)\) \(\chi_{8015}(3347,\cdot)\) \(\chi_{8015}(3487,\cdot)\) \(\chi_{8015}(3662,\cdot)\) \(\chi_{8015}(3718,\cdot)\) \(\chi_{8015}(4152,\cdot)\) \(\chi_{8015}(4208,\cdot)\) \(\chi_{8015}(4383,\cdot)\) \(\chi_{8015}(4558,\cdot)\) \(\chi_{8015}(4593,\cdot)\) \(\chi_{8015}(4817,\cdot)\) \(\chi_{8015}(5412,\cdot)\) \(\chi_{8015}(5517,\cdot)\) \(\chi_{8015}(5818,\cdot)\) \(\chi_{8015}(6077,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{76})$ |
| Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\((3207,4581,4586)\) → \((i,1,e\left(\frac{61}{76}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(11\) | \(12\) | \(13\) | \(16\) |
| \( \chi_{ 8015 }(22, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{53}{76}\right)\) | \(e\left(\frac{4}{19}\right)\) | \(e\left(\frac{61}{76}\right)\) | \(e\left(\frac{6}{19}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{1}{38}\right)\) | \(e\left(\frac{69}{76}\right)\) | \(e\left(\frac{25}{38}\right)\) | \(e\left(\frac{8}{19}\right)\) |